Convex quadratic problem solving method and device of DR segmentation-gradient descent model based on algorithm expansion

Abstract

The invention discloses a convex quadratic problem solving method of a DR segmentation-gradient descent model based on algorithm expansion, and belongs to the technical field of deep learning. The method comprises the following steps: acquiring a data set of a convex quadratic problem; the data set is input into a trained DR segmentation-gradient descent model, a predicted solution of the DR segmentation-gradient descent model of the convex quadratic problem is obtained, and the predicted solution of the DR segmentation-gradient descent model is obtained by adopting an L2O algorithm to expand and solve the DR segmentation-gradient descent model; and inputting a prediction solution of the DR segmentation-gradient descent model into a hot start point of an SCS solver to obtain a target solution of a convex quadratic problem. According to the method, the calculation cost and time for solving the minimum power generation cost problem are reduced.

Description

Technical Field

[0001] This application belongs to the technical field of deep learning, and particularly relates to a method and device for solving convex quadratic problems of a DR segmentation-gradient descent model based on algorithm expansion. Background Art

[0002] In the scenario of calculating the optimal grid cost, the convex quadratic optimization problem solving method, as the core technology of grid optimization, its calculation efficiency directly determines the real-time performance of the grid decision-making system and the feasibility of large-scale grid engineering problems. The linear system solving bottleneck of traditional iterative algorithms in high-dimensional parameter spaces may lead to computational delays in the optimization process, thereby causing decision lags and inaccurate resource allocation. Therefore, constructing a new solving framework that takes into account both computational efficiency and theoretical guarantees has become the key path to breaking through the optimization bottleneck of complex systems.

[0003] The existing solutions to convex quadratic optimization problems mainly rely on classical numerical algorithms and learning optimization paradigms, but there are still significant performance limitations. Firstly, the traditional DR segmentation algorithm has a cubic computational complexity in matrix inversion operations, making it difficult to meet the real-time solving requirements in the scenario of dimensional explosion. Secondly, although the acceleration technology based on L2O has the advantage of data-driven, it has insufficient generalization adaptability to problem structures and there is an inherent contradiction in the decoupling of algorithm expansion and theoretical convergence guarantee. In addition, the optimization model of the hybrid architecture adopts a mechanism that separates explicit iteration and implicit learning, lacking the ability to fuse computational graphs in dynamic scenarios, resulting in memory consumption and inference delay problems when solving large-scale convex quadratic optimization problems.

[0004] The current convex quadratic optimization problem solving methods face multiple technical obstacles in the application of calculating the optimal grid cost. Existing algorithms are difficult to effectively balance the dialectical relationship between computational accuracy and time cost, have weak adaptability to high-dimensional parameter spaces, and generally have problems such as excessive matrix operation redundancy, insufficient algorithm generalization ability, and lack of theoretical convergence. Especially when dealing with large-scale convex quadratic optimization problems, there are problems such as low efficiency, high computational cost, and long computational time. Summary of the Invention

[0005] This application aims to at least solve one of the technical problems existing in the prior art. For this purpose, this application proposes a method and device for solving convex quadratic problems of a DR segmentation-gradient descent model based on algorithm expansion, which reduces the computational cost and time when solving the minimum power generation cost problem.

[0006] In a first aspect, this application provides a method for solving convex quadratic problems of a DR segmentation-gradient descent model based on algorithm expansion, the method comprising:

[0007] Obtain a data set of convex quadratic problems;

[0008] Input the dataset into the trained DR segmentation - gradient descent model to obtain the predicted solution of the DR segmentation - gradient descent model for the convex quadratic problem. The predicted solution of the DR segmentation - gradient descent model is obtained by solving using the L2O algorithm in the DR segmentation - gradient descent model;

[0009] Input the predicted solution of the DR segmentation - gradient descent model into the warm - start point of the SCS solver to obtain the objective solution of the convex quadratic problem.

[0010] According to an embodiment of the present application, the calculation formula of the DR segmentation - gradient descent model is as follows:

[0011]

[0012] where w k is the historical variable, u k+1 is the intermediate variable, M is the first problem parameter of the dataset, is the updated variable, q is the second problem parameter of the dataset, and I is the identity matrix.

[0013] According to an embodiment of the present application, the calculation formula of the DR segmentation - gradient descent model expanded using the L2O algorithm is as follows:

[0014]

[0015] where is the formula after adding learnable parameters to the gradient of the least - squares problem, I is the identity matrix, is the first intermediate iteration variable, is the second intermediate iteration variable, is the first learnable parameter, q is the second problem parameter of the dataset, is the second intermediate iteration variable, is the third intermediate iteration variable, σ is the sigmoid function, is the second learnable parameter, is the third learnable parameter, is the width of the network layer, M is the first problem parameter of the dataset, is the learnable step - size parameter, I, is a vector with all elements equal to 1 and dimension of

[0016] According to an embodiment of the present application, the training process of the DR segmentation - gradient descent model includes:

[0017] Construct a preset DR segmentation - gradient descent model;

[0018] Obtain the dataset of the convex quadratic problem as the training set;

[0019] Based on the loss function, the preset DR segmentation - gradient descent model is trained according to the training set to obtain the DR segmentation - gradient descent model.

[0020] According to an embodiment of the present application, the loss function is established based on the distance between the predicted solution and the target solution of the DR segmentation - gradient descent model, and the calculation formula of the loss function is as follows:

[0021]

[0022] where is the data set, (x i , y i ) is the predicted solution of the DR segmentation - gradient descent model, is the target solution.

[0023] According to an embodiment of the present application, the solving process of the target solution includes:

[0024] Input the convex quadratic problem and the predicted solution of the DR segmentation - gradient descent model into the SCS solver;

[0025] Based on the KKT conditions, the target solution satisfying the convex quadratic problem is obtained.

[0026] According to an embodiment of the present application, the KKT conditions include:

[0027]

[0028] where A is the first parameter, (x, y) is the solution of the convex quadratic problem, s is the first variable, b is the third parameter, P is the fourth parameter, and c is the fifth parameter.

[0029] In a second aspect, the present application provides a device for solving the convex quadratic problem of the DR segmentation - gradient descent model based on algorithm expansion, and the device includes:

[0030] An acquisition module, configured to acquire a data set of the convex quadratic problem;

[0031] A first solving module, configured to input the data set into the trained DR segmentation - gradient descent model to obtain the predicted solution of the convex quadratic problem of the DR segmentation - gradient descent model, and the predicted solution of the DR segmentation - gradient descent model is obtained by solving using the L2O algorithm expansion of the DR segmentation - gradient descent model;

[0032] A second solving module, configured to input the predicted solution of the DR segmentation - gradient descent model into the warm - start point of the SCS solver to obtain the target solution of the convex quadratic problem.

[0033] In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion as described in the first aspect above is implemented.

[0034] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion as described in the first aspect above is implemented.

[0035] In a fifth aspect, the present application provides a chip, which includes a processor and a communication interface. The communication interface is coupled to the processor, and the processor is used to run a program or an instruction to implement the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion as described in the first aspect.

[0036] In a sixth aspect, the present application provides a computer program product, including a computer program. When the computer program is executed by a processor, the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion as described in the first aspect above is implemented.

[0037] Additional aspects and advantages of the present application will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present application.

[0038] The method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion provided by the present invention has the following beneficial effects compared with the prior art:

[0039] (1) By using the L2O algorithm expansion, each iteration step of the DR segmentation-gradient descent model is transformed into a layer in the neural network, realizing end-to-end training to automatically optimize the update strategy of each iteration, improving the generality of the DR segmentation-gradient descent model. By introducing a warm start module, the computational efficiency is further accelerated when solving the same problem or similar problems multiple times. Using the historical solution or the model prediction solution as the prediction solution of the DR segmentation-gradient descent model reduces the time of each solution, simplifies the calculation process, improves the computational efficiency, makes the optimization process more efficient, reduces the number of iterations, reduces the solution cost, improves the accuracy of the target solution, and reduces the computational cost and time when solving the grid cost optimization problem.

[0040] (2) By introducing the gradient descent method to replace the linear system solving step in the traditional DR segmentation algorithm, the present invention significantly reduces the computational complexity, improves the efficiency of solving convex quadratic problems, reduces the computational time and cost, and is applicable to solving large-scale power grid problems.

[0041] (3) Through the algorithm expansion method based on the L2O neural network, each iteration step of the DR segmentation - gradient descent algorithm is transformed into a layer in the neural network, and the update strategy of each iteration is automatically optimized through end-to-end training. This improves the generality of the DR segmentation - gradient descent algorithm and can be applied to convex quadratic optimization problems in different fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The above and / or additional aspects and advantages of the present application will become apparent and be readily understood from the following description of embodiments in conjunction with the accompanying drawings, where:

[0043] Figure 1 is one of the flow diagrams of the method for solving convex quadratic problems of the DR segmentation - gradient descent model based on algorithm expansion provided by the embodiment of the present application;

[0044] Figure 2 is another flow diagram of the method for solving convex quadratic problems of the DR segmentation - gradient descent model based on algorithm expansion provided by the embodiment of the present application;

[0045] Figure 3 is the flow diagram of the solution of the DR segmentation - gradient descent model provided by the embodiment of the present application;

[0046] Figure 4 is the structural diagram of one layer of the DR segmentation - gradient descent network provided by the embodiment of the present application;

[0047] Figure 5 is the flow chart of the training process of the DR segmentation - gradient descent model provided by the embodiment of the present application;

[0048] Figure 6 is the flow diagram of the warm start provided by the embodiment of the present application;

[0049] Figure 7 is the structural diagram of the device for solving convex quadratic problems of the DR segmentation - gradient descent model based on algorithm expansion provided by the embodiment of the present application;

[0050] Figure 8 is the structural diagram of the electronic device provided by the embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] Next, the technical solutions in the embodiments of the present application will be clearly described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.

[0052] The terms "first", "second", etc. in the description and claims of the present application are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same category, and do not limit the number of objects. For example, the first object can be one or multiple. In addition, "and / or" in the description and claims means at least one of the connected objects, and the character " / " generally represents an "or" relationship between the associated objects before and after.

[0053] Next, in conjunction with the accompanying drawings, through specific embodiments and their application scenarios, the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on an algorithm, the device for solving the convex quadratic problem of the DR segmentation-gradient descent model based on an algorithm, an electronic device, and a readable storage medium provided in the embodiments of the present application will be described in detail.

[0054] Among them, the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on an algorithm can be applied to a terminal, and can be specifically executed by hardware or software in the terminal.

[0055] The terminal includes, but is not limited to, portable communication devices such as mobile phones or tablet computers having a touch-sensitive surface (for example, a touch screen display and / or a touchpad). It should also be understood that in some embodiments, the terminal may not be a portable communication device, but a desktop computer having a touch-sensitive surface (for example, a touch screen display and / or a touchpad).

[0056] In the following various embodiments, a terminal including a display and a touch-sensitive surface is described. However, it should be understood that the terminal may include one or more other physical user interface devices such as a physical keyboard, a mouse, and a joystick.

[0057] The convex quadratic problem solving method of the DR segmentation-gradient descent model based on algorithm expansion provided by the embodiments of the present application. The execution subject of the convex quadratic problem solving method of the DR segmentation-gradient descent model based on algorithm expansion can be an electronic device or a functional module or functional entity in the electronic device that can implement the convex quadratic problem solving method of the DR segmentation-gradient descent model based on algorithm expansion. The electronic devices mentioned in the embodiments of the present application include, but are not limited to, mobile phones, tablet computers, computers, cameras, and wearable devices, etc. Here, taking the electronic device as the execution subject, the convex quadratic problem solving method of the DR segmentation-gradient descent model based on algorithm expansion provided by the embodiments of the present application will be described.

[0058] The convex quadratic optimization problem is an optimization problem widely used in the power grid field, and control problems in engineering are often transformed into convex quadratic optimization problems for solution. The convex quadratic optimization problem usually has a convex quadratic objective function and is restricted by linear constraint conditions. The convex quadratic optimization problem is also often used for the step-by-step approximation of non-convex problems, such as by constructing sequential convex approximations or relaxing non-convex problems. Due to the good mathematical structure of the convex quadratic optimization problem, many optimization algorithms are based on the solution methods of convex quadratic optimization problems, such as the active set method and the interior point method, etc. However, as the problem scale increases, the computational complexity of traditional algorithms gradually becomes a bottleneck, especially in the case of high-dimensional and large-scale constraint conditions.

[0059] The traditional DR (Douglas-Rachford) segmentation algorithm is an iterative solution method based on reflection and projection, usually used to solve linear constraint quadratic optimization problems. The advantage of the DR algorithm lies in its good convergence and strong adaptability to many problems. However, in each iteration, the algorithm needs to solve a linear system. As the problem scale increases, the computational amount of solving these linear systems increases significantly, resulting in low algorithm efficiency, especially prominent in high-dimensional data and large-scale problems.

[0060] In recent years, the L2O (Learning-to-Optimize) method has gradually emerged in the optimization field, accelerating traditional optimization algorithms through machine learning. The idea of L2O is to learn the optimization strategy of specific problems by training a model, thus exceeding the performance of traditional methods. This method usually requires a large amount of training data and often relies on adjusting the optimization strategy through supervised learning during the iterative training process.

[0061] Although the L2O method can significantly accelerate the optimization process under certain conditions, it generally lacks theoretical convergence guarantees, and when solving large-scale convex quadratic optimization problems, the computational cost and inference speed are still challenges. Although traditional DR splitting algorithms perform well in solving small-scale convex quadratic optimization problems, due to the need to solve linear systems in each iteration, the computational complexity gradually increases in large-scale problems, making it difficult to meet the efficiency requirements in practical applications. Although the L2O method can accelerate the optimization process, it does not learn deeply enough about the specific characteristics of the optimization problem and lacks theoretical support for convergence, resulting in unstable performance when dealing with large-scale convex quadratic optimization problems.

[0062] Existing algorithms have computational bottlenecks when solving large-scale convex quadratic optimization problems, especially the high computational cost of solving linear systems. Although techniques based on algorithm unfolding can accelerate the optimization process by transforming the iterative steps of traditional optimization algorithms into layers in a neural network, thus enabling end-to-end training and optimization, in traditional DR splitting algorithms, the step of solving the linear system becomes a limiting factor. This is because the iteration of traditional DR splitting algorithms depends on the solution of matrices, and this solution step is not easily transformed into a fixed neural network structure, thereby hindering the effective implementation of algorithm unfolding.

[0063] Therefore, although algorithm unfolding can accelerate the optimization process, in the step of solving the linear system, unfolding is not easily achieved, thus affecting the effectiveness of the unfolding technique. The main defects of the existing technologies are as follows:

[0064] Traditional algorithms have high computational complexity, especially the step of solving the linear system in large-scale convex quadratic optimization problems leads to low efficiency;

[0065] Existing learning optimization algorithms (L2O) have poor universality, can only be optimized for specific problems, and directly based on the algorithm unfolding of DR-Splitting, due to the challenges in the step of solving the linear system.

[0066] Figure 1 It is one of the flow diagrams of the method for solving convex quadratic problems of the DR splitting-gradient descent model based on algorithm unfolding provided by the embodiments of the present application. As Figure 1 shown, the method for solving convex quadratic problems of the DR splitting-gradient descent model based on algorithm unfolding includes: step 110, step 120, and step 130.

[0067] Step 110, obtain a data set of convex quadratic problems;

[0068] It is easy to understand that a convex quadratic problem is an optimization problem with a convex quadratic objective function and linear constraints, which is widely used in fields such as control system optimization and power grid optimization. The calculation formula of the objective function of the convex quadratic problem is as follows:

[0069]

[0070] Among them, x is the independent variable, y is the dependent variable, P is the first parameter of the convex quadratic problem, and c is the second parameter of the convex quadratic problem.

[0071] The calculation formula for the constraints of the convex quadratic problem is as follows:

[0072]

[0073] Among them, A is the first parameter, x is the independent variable, s is the first variable, and b is the third parameter.

[0074] In some embodiments, the minimum power generation cost of the power grid can be solved by the convex quadratic problem. At this time, the data set includes the power generation cost data and the power generation power data of the power grid under different operating states.

[0075] Step 120: Input the data set into the trained DR splitting-gradient descent model to obtain the predicted solution of the DR splitting-gradient descent model for the convex quadratic problem. The predicted solution of the DR splitting-gradient descent model is obtained by the DR splitting-gradient descent model using the L2O algorithm for solution;

[0076] It is easy to understand that the DR splitting algorithm can be used for an iterative algorithm to solve optimization problems with linear constraints and quadratic objectives, and is widely used to calculate reflection operators and projection operators, and converges to the optimal solution by gradually updating the approximate solution.

[0077] The DR splitting-gradient descent model includes the DR splitting algorithm and the gradient descent algorithm, which simplifies the calculation process through the gradient descent algorithm.

[0078] Taking the solution of the minimum power generation cost of the power grid as an example, when using the DR splitting-gradient descent model to solve the minimum power generation cost of the power grid, the L2O algorithm is used for expansion. The expansion of the L2O algorithm is a method that transforms the iterative steps of the classical optimization algorithm into network layers in the neural network. Each step of the iterative optimization algorithm can be transformed into a layer in the neural network, so as to achieve end-to-end training. Step 130: Input the predicted solution of the DR splitting-gradient descent model into the warm start point of the SCS solver to obtain the target solution of the convex quadratic problem.

[0079] It should be noted that SCS (Splitting Conic Solver), a splitting conic solver, is an efficient solver for convex optimization problems and uses an adaptive splitting method to solve problems. SCS is particularly suitable for optimization problems containing cone constraints.

[0080] Figure 2This is the second flowchart diagram of the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on an algorithm provided by an embodiment of the present application. As Figure 2 shown, taking the solution of the minimum power generation cost of the power grid as an example, first, the power generation cost and power generation power data of the power grid are obtained as a data set, and input into the model training module to train the preset DR segmentation-gradient descent model, obtaining the trained DR segmentation-gradient descent model. Based on the minimum power generation cost of the power grid, a target problem is constructed, and the target problem is input into the model prediction module to obtain the predicted solution of the DR segmentation-gradient descent model. Finally, the predicted solution of the DR segmentation-gradient descent model is input into the warm start module to obtain the optimal solution of the target problem.

[0081] According to the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on an algorithm provided by an embodiment of the present application, by using the L2O algorithm to expand and converting each iteration step of the DR segmentation-gradient descent model into a layer in the neural network, the end-to-end training is realized to automatically optimize the update strategy of each iteration, improving the generality of the DR segmentation-gradient descent model. By introducing the warm start module, the computational efficiency is further accelerated when solving the same problem or similar problems multiple times. Using the historical solution or the predicted solution of the model as the predicted solution of the DR segmentation-gradient descent model reduces the time for each solution, simplifies the calculation process, improves the computational efficiency, makes the optimization process more efficient, reduces the number of iterations, reduces the solution cost, improves the accuracy of the target solution, and reduces the computational cost and time when solving the power grid cost optimization problem.

[0082] In some embodiments, the calculation formula of the DR segmentation-gradient descent model is as follows:

[0083]

[0084] where w k is the historical variable, u k+1 is the intermediate variable, M is the first problem parameter of the data set, is the update variable, q is the second problem parameter of the data set, and I is the identity matrix.

[0085] It should be noted that the DR segmentation-gradient descent model first combines the problem parameters in the target problem into the data form required in the network. Figure 3 This is the flowchart diagram of the solution of the DR segmentation-gradient descent model provided by an embodiment of the present application. As Figure 3 shown, the target problem parameters P, A, c, and b are combined into matrix M and vector q, and the combination calculation formula is as follows:

[0086]

[0087] The process of the DR segmentation algorithm includes the following steps:

[0088] (1) Initialize w 0 = 0,

[0089] (2) Update the intermediate variable based on the resolvent operator

[0090]

[0091] (3) After reflecting with respect to w k project it onto on

[0092]

[0093] (4) Update the iterative variable w k based on the historical variable w k+1 and the intermediate variable u k+1

[0094]

[0095] (5) Output the final solution, u k = (x k , y k )

[0096] The DR segmentation - gradient algorithm replaces the first step involving matrix inversion in the original DR algorithm with a one - step gradient descent update of its corresponding unconstrained least - squares problem. The specific steps are as follows:

[0097] (1) The calculation formula for the unconstrained least - squares problem is as follows:

[0098]

[0099] (2) Calculate the gradient direction

[0100]

[0101] (3) Determine the step size η through line search k

[0102] (4) Update by advancing along the gradient direction

[0103]

[0104] The remaining steps are the same as those of the above DR segmentation algorithm

[0105] Figure 4This is a schematic diagram of a layer of the DR segmentation-gradient descent network provided by the embodiments of the present application. As Figure 4 shown, the parameters in the gray part are input parameters, and the parameters in the blue part are learnable parameters.

[0106] In this embodiment, by introducing the gradient descent method to replace the linear system solving step in the traditional DR segmentation algorithm, the computational complexity is significantly reduced, the efficiency of solving the convex quadratic problem is improved, the computing time and computing cost are reduced, and it is applicable to large-scale power grid problem solving.

[0107] In some embodiments, the calculation formula of the DR segmentation-gradient descent model expanded by the L2O algorithm is as follows:

[0108]

[0109] Among them, is the formula after adding learnable parameters to the gradient of the least squares problem, I is the identity matrix, is the first intermediate iteration variable, is the second intermediate iteration variable, is the first learnable parameter, q is the second problem parameter of the data set, is the second intermediate iteration variable, is the third intermediate iteration variable, σ is the sigmoid function, is the second learnable parameter, is the third learnable parameter, is the width of the network layer, M is the first problem parameter of the data set, is the learnable step size parameter, I, is the vector with all elements being 1 in dimension of.

[0110] It should be noted that based on the DR segmentation-gradient descent algorithm, the L2O algorithm is used for expansion, and learnable parameters are introduced. These parameters will be updated during the training process. The specific steps of the L20 algorithm for expanding the DR segmentation-gradient descent algorithm are as follows:

[0111] (1) Initialization:

[0112]

[0113] (2) Update

[0114]

[0115] Among them, ⊙ represents element-wise multiplication between vectors.

[0116] (3) Update

[0117]

[0118] (4) Update

[0119]

[0120] (5) Output solution

[0121]

[0122] In this embodiment, through the algorithm expansion method based on the L2O neural network, each iteration step of the DR segmentation - gradient descent algorithm is transformed into a layer in the neural network, and the update strategy of each iteration is automatically optimized through end - to - end training. The generality of the DR segmentation - gradient descent algorithm is improved, and it can be applied to convex quadratic optimization problems in different fields.

[0123] In some embodiments, the training process of the DR segmentation - gradient descent model includes:

[0124] Construct a preset DR segmentation - gradient descent model;

[0125] Obtain the data set of the convex quadratic problem as the training set;

[0126] Based on the loss function, train the preset DR segmentation - gradient descent model according to the training set to obtain the DR segmentation - gradient descent model.

[0127] It is easy to understand that the DR segmentation - gradient descent model is trained in a supervised manner. Figure 5 is a flowchart of the training process of the DR segmentation - gradient descent model provided by the embodiments of the present application. As Figure 5 shown, specifically, in each training step, the problems in the data set are input into the prediction module of the DR segmentation - gradient descent model to obtain predicted solutions. These predicted solutions are compared with the collected labels, and the loss function is calculated to update the DR segmentation - gradient descent model. Through such cyclic update operations, when the number of cycles reaches a preset threshold, the trained model is output.

[0128] In this embodiment, by constructing a preset DR segmentation - gradient descent model and obtaining the data set of the convex quadratic problem as the training set, sufficient data support can be provided for model training. During the training process, the model is optimized based on the loss function. By adjusting the parameters of the training set and the loss function, a trained DR segmentation - gradient descent model can be obtained in a relatively short time, reducing unnecessary iterations and computational costs.

[0129] In some embodiments, the loss function is established based on the distance between the predicted solution of the DR splitting-gradient descent model and the target solution, and the calculation formula of the loss function is as follows:

[0130]

[0131] Where is the dataset, (x i , y i ) is the predicted solution of the DR splitting-gradient descent model, is the target solution.

[0132] In this embodiment, the loss function is constructed based on the distance between the predicted solution of the DR splitting-gradient descent model and the target solution. When the value of the loss function reaches a certain threshold, it indicates that the model has converged, reducing the computational cost and time, improving the prediction accuracy and efficiency of the DR splitting-gradient descent model, and enhancing the robustness and stability of the DR splitting-gradient descent model in practical applications.

[0133] In some embodiments, the solution process of the target solution includes:

[0134] Input the convex quadratic problem and the predicted solution of the DR splitting-gradient descent model into the SCS solver;

[0135] Based on the KKT conditions, obtain the target solution that satisfies the convex quadratic problem.

[0136] It should be noted that although the predicted solution of the DR splitting-gradient descent model obtained by the DR splitting-gradient descent model can be as close as possible to the optimal solution of the convex quadratic problem, for constrained optimization problems, it usually cannot satisfy the constraints of the problem. Therefore, the predicted solution of the DR splitting-gradient descent model is input into the SCS solver to obtain the warm start solution as the final target solution, which can accelerate the solution process and accuracy of the problem as much as possible while satisfying feasibility.

[0137] Figure 6 is the schematic flow chart of the warm start provided by the embodiments of the present application. As Figure 6 shown, in some embodiments, the target problem and the predicted solution of the DR splitting-gradient descent model are input into a DR-splitting-based solver such as SCS to obtain the optimal solution of the target problem.

[0138] In this embodiment, inputting the convex quadratic problem and the predicted solution of the DR splitting-gradient descent model into the SCS solver can further accelerate the computational efficiency when solving the same problem or similar problems multiple times. By using the historical solution or the model predicted solution as the predicted solution of the DR splitting-gradient descent model, the time and computational cost of each solution are reduced.

[0139] In some embodiments, the KKT conditions include:

[0140]

[0141] where A is the first parameter, (x, y) is the solution of the convex quadratic problem, s is the first variable, b is the third parameter, P is the fourth parameter, and c is the fifth parameter.

[0142] It is easy to understand that the KKT (Karush-Kuhn-Tucker, optimality conditions for quadratic programming) conditions are necessary and sufficient conditions for the optimality of the convex quadratic problem.

[0143] In some embodiments, the calculation formula for the data set is as follows:

[0144]

[0145] Since P ≥ 0, and That is, M is monotonic. Therefore, the KKT conditions can be expressed as the following monotone inclusion problem:

[0146]

[0147] where is the normal cone of.

[0148] The calculation formula for is as follows:

[0149]

[0150] At this time, the optimal solution of the convex quadratic optimization problem can be obtained by solving the above monotone inclusion problem.

[0151] In this embodiment, by introducing the KKT conditions, the feasibility and optimality of the solution can be constrained, the accuracy of solving the convex quadratic problem is improved, unnecessary calculation processes are reduced, and when the KKT conditions are satisfied, it can be determined in advance that the solution of the convex quadratic problem has reached the optimal solution, reducing the redundant iteration process, as well as the calculation cost and time, and improving the efficiency and robustness of solving the convex quadratic problem.

[0152] For the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion provided in the embodiments of the present application, the execution subject can be a device for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion. In the embodiments of the present application, taking the device for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion executing the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion as an example, the device for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion provided in the embodiments of the present application is described.

[0153] The embodiments of the present application further provide a convex quadratic problem solving device for a DR segmentation-gradient descent model based on algorithm expansion, as Figure 7 shown. The convex quadratic problem solving device for the DR segmentation-gradient descent model based on algorithm expansion includes: an acquisition module 710, a first solving module 720, and a second solving module 730.

[0154] The acquisition module 710 is configured to acquire a data set of the convex quadratic problem;

[0155] The first solving module 720 is configured to input the data set into a trained DR segmentation-gradient descent model to obtain a predicted solution of the DR segmentation-gradient descent model for the convex quadratic problem, and the predicted solution of the DR segmentation-gradient descent model is obtained by solving using the L2O algorithm for the DR segmentation-gradient descent model;

[0156] The second solving module 730 is configured to input the predicted solution of the DR segmentation-gradient descent model into the warm start point of the SCS solver to obtain the target solution of the convex quadratic problem.

[0157] According to the convex quadratic problem solving method for the DR segmentation-gradient descent model based on algorithm expansion provided by the embodiments of the present application, by using the L2O algorithm to expand and converting each iteration step of the DR segmentation-gradient descent model into a layer in a neural network, end-to-end training is realized to automatically optimize the update strategy of each iteration, improving the versatility of the DR segmentation-gradient descent model. By introducing a warm start module, the computational efficiency is further accelerated when solving the same problem or similar problems multiple times. Using the historical solution or the model predicted solution as the predicted solution of the DR segmentation-gradient descent model reduces the time for each solution, simplifies the calculation process, improves the computational efficiency, makes the optimization process more efficient, reduces the number of iterations, reduces the solution cost, improves the accuracy of the target solution, and reduces the computational cost and time when solving the grid cost optimization problem.

[0158] The convex quadratic problem solving device for the DR segmentation-gradient descent model based on algorithm expansion provided by the embodiments of the present application can implement Figures 1 to 6 each process implemented by the convex quadratic problem solving method embodiment of the DR segmentation-gradient descent model based on algorithm expansion. To avoid repetition, it will not be elaborated here.

[0159] In some embodiments, as Figure 8As shown in the figure, an embodiment of the present application further provides an electronic device 800, which includes a processor 801, a memory 802, and a computer program stored on the memory 802 and executable on the processor 801. When the program is executed by the processor 801, it implements each process of the above-mentioned embodiment of the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on the algorithm, and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.

[0160] It should be noted that the electronic device in the embodiment of the present application includes the above-mentioned mobile electronic device and non-mobile electronic device.

[0161] An embodiment of the present application further provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements each process of the above-mentioned embodiment of the method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on the algorithm, and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.

[0162] Among them, the processor is the processor in the electronic device in the above-mentioned embodiment. The readable storage medium includes computer-readable storage media, such as computer read-only memory (Read-Only Memory, ROM), random access memory (RandomAccess Memory, RAM), magnetic disk or optical disc, etc.

[0163] An embodiment of the present application further provides a computer program product, including a computer program, which implements the above-mentioned method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on the algorithm when executed by a processor.

[0164] Among them, the processor is the processor in the electronic device in the above-mentioned embodiment. The readable storage medium includes computer-readable storage media, such as computer read-only memory ROM, random access memory RAM, magnetic disk or optical disc, etc.

[0165] Another embodiment of the present application provides a chip, which includes a processor and a communication interface. The communication interface is coupled to the processor, and the processor is used to run a program or instruction to implement each process of the above-mentioned embodiment of the method for solving the convex quadratic problem of the DR segmentation-gradient descent model, and can achieve the same technical effect. To avoid repetition, it will not be elaborated here.

[0166] It should be understood that the chip mentioned in the embodiment of the present application can also be called a system-on-chip, system chip, chip system, or system-on-chip, etc.

[0167] It should be noted that in this article, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "comprising a..." does not exclude the presence of additional identical elements in the process, method, article or device comprising such element. In addition, it should be pointed out that the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in the reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. Additionally, the features described with reference to certain examples may be combined in other examples.

[0168] Through the description of the above embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a computer software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to enable a terminal (which can be a mobile phone, computer, server, or network device, etc.) to execute the convex quadratic problem solving method of the DR segmentation-gradient descent model based on algorithms in each embodiment of the present application.

[0169] In the description of the present application, "the first feature", "the second feature" may include one or more of such features.

[0170] In the description of the present application, the meaning of "a plurality of" is two or more.

[0171] The embodiments of the present application have been described above in conjunction with the accompanying drawings. However, the present application is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Those of ordinary skill in the art, under the inspiration of the present application and without departing from the spirit and scope protected by the claims of the present application, can also make many forms, all of which fall within the protection scope of the present application.

[0172] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "schematic embodiments", "examples", "specific examples", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0173] Although the embodiments of this application have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and purposes of this application, and the scope of this application is defined by the claims and their equivalents.

Claims

1. A method for solving convex quadratic problems of a DR segmentation-gradient descent model based on algorithm expansion, characterized in that The method includes: Obtaining a data set of a convex quadratic problem; Inputting the data set into a trained DR splitting-gradient descent model to obtain a predicted solution of the DR splitting-gradient descent model for the convex quadratic problem, where the predicted solution of the DR splitting-gradient descent model is obtained by solving using the L2O algorithm in the DR splitting-gradient descent model; Inputting the predicted solution of the DR splitting-gradient descent model into the warm start point of the SCS solver to obtain the target solution of the convex quadratic problem.

2. The method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion according to claim 1, characterized in that, The calculation formula of the DR splitting-gradient descent model is as follows: where, w k is a historical variable, u k+1 is an intermediate variable, M is the first problem parameter of the data set, is an update variable, q is the second problem parameter of the data set, I is the identity matrix, η k is an intermediate iteration variable, t k is the time step.

3. The method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion according to claim 1, characterized in that, The calculation formula of the DR splitting-gradient descent model using the L2O algorithm is as follows: Among them, g l is the formula after adding learnable parameters to the gradient of the least squares problem, I is the identity matrix, is the first intermediate iteration variable, w l-1 is the second intermediate iteration variable, is the first learnable parameter, q is the second problem parameter of the dataset, is the second intermediate iteration variable, η l is the third intermediate iteration variable, σ is the sigmoid function, is the second learnable parameter, is the third learnable parameter, d l is the width of the network layer, M is the first problem parameter of the dataset, η l is the learnable step size parameter, is of dimension d l and is a vector with all elements equal to 1.

4. The method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion according to claim 1, characterized in that, The training process of the DR splitting-gradient descent model includes: Constructing a preset DR splitting-gradient descent model; Obtaining the data set of the convex quadratic problem as a training set; Based on the loss function, training the preset DR splitting-gradient descent model according to the training set to obtain the DR splitting-gradient descent model.

5. The method for solving the convex quadratic problem of the DR segmentation-gradient descent model expanded based on an algorithm according to claim 4, characterized in that The loss function is established based on the distance between the predicted solution of the DR splitting-gradient descent model and the target solution, and the calculation formula of the loss function is as follows: Among them, is the data set, (x i , y i ) is the predicted solution of the DR segmentation-gradient descent model, is the target solution.

6. The method for solving the convex quadratic problem of the DR segmentation-gradient descent model based on algorithm expansion according to claim 1, characterized in that, The solving process of the target solution includes: Inputting the convex quadratic problem and the predicted solution of the DR splitting-gradient descent model into the SCS solver; Based on the KKT conditions, obtaining the target solution that satisfies the convex quadratic problem.

7. The method for solving the convex quadratic problem of the DR segmentation-gradient descent model expanded based on the algorithm according to claim 6, characterized in that, The KKT conditions include: Where A is the first parameter, (x, y) is the solution of the convex quadratic problem, s is the first variable, b is the third parameter, P is the fourth parameter, and c is the fifth parameter.

8. A convex quadratic problem solving device for a DR segmentation-gradient descent model based on algorithm expansion, which is implemented by using the convex quadratic problem solving method for the DR segmentation-gradient descent model based on algorithm expansion according to any one of claims 1 to 7, and is characterized in that, The device includes: An acquisition module for obtaining a data set of a convex quadratic problem; A first solving module for inputting the data set into a trained DR splitting-gradient descent model to obtain a predicted solution of the DR splitting-gradient descent model for the convex quadratic problem, where the predicted solution of the DR splitting-gradient descent model is obtained by solving using the L2O algorithm in the DR splitting-gradient descent model; A second solving module for inputting the predicted solution of the DR splitting-gradient descent model into the warm start point of the SCS solver to obtain the target solution of the convex quadratic problem.

9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method for solving the convex quadratic problem of the DR splitting-gradient descent model based on the algorithm as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by the processor, it implements the method for solving the convex quadratic problem of the DR splitting-gradient descent model based on the algorithm as described in any one of claims 1 to 7.

Images