Nonlinear optimization method and storage medium

Abstract

A nonlinear optimization method and a storage medium, wherein the method includes the steps of establishing a linearization model according to the nonlinear optimization problem; solving the linearization model through a first-order iterative algorithm, continuously reducing the error between the nonlinear optimization problem and the linearization model, and finally finding Feasible solutions of nonlinear problems under a certain target value; through the second-order iterative algorithm, the target value of the nonlinear problem is continuously updated to find the feasible solution of the problem with the maximum target value, that is, the solution of the nonlinear optimization problem. Robust, efficient, actuarial computation for solving large-scale nonlinear problems.

Description

technical field [0001] The invention relates to the field of computer program design, in particular to an algorithm and a storage medium for large-scale calculation of nonlinear problems. Background technique [0002] Nonlinear constrained optimization problems are the most general form of optimization problems. The optimization algorithms for solving such problems can be divided into two categories: deterministic algorithms (linear constraint problem algorithm extension, penalty function method and sequential quadratic programming method), intelligent algorithms (simulated annealing, genetic algorithm, tabu search, artificial neural network Wait). [0003] (1) The algorithm for linear constraint problems is extended to nonlinear constraint problems. Including generalized elimination method, feasible direction method, generalized reduced gradient method and projected gradient method, etc. The main idea is: do not convert the original constrained optimization problem in ad...

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Problems solved by technology

[0013] (1) The contradiction between effectiveness and accuracy: When existing algorithms solve large-scale problems, they need to solve the problem quickly or within an acceptable calculation time (that is, to improve effectiveness), which may cause the results to be different from the actual situation. There is a large error (i.e. reduced accuracy)

[0014] (2) The contradiction between robustness and effectiveness: In order to accurately find solutions to large-scale optimization problems, existing algorithms must adopt a large number of rules and strategies to achieve a reasonable selection of initial solutions and effective convergence of the algorithm (that is, to improve robustness), And this is bound to spend a lot of computing time, reducing the effectiveness of the algorithm

However, this kind of algorithm needs to solve a series of linear programming, quadratic programming or unconstrained optimization problems to approach the original problem successively, which requires a large amount of calculation and slow convergence speed. What is more serious is that as the scale of the problem increases exponentially with the number of variables, these The convergence ability of the algorithm is getting worse and worse, which makes it difficult to solve it exactly

[0017] (2) Intelligent algorithms (simulated annealing, genetic algorithm, tabu search, artificial neural network, etc.), under the condition that the function structure of the existing problem remains unchanged, use a large number of heuristic rules, which can be qualitatively analyzed but difficult to prove quantitatively, and large Most algorithms are based on random characteristics, and the selection of initial solutions and algorithm convergence are difficult to estimate

When solving large-scale nonlinear optimization problems, its convergence is generally in the sense of probability, the actual performance is uncontrollable, the convergence speed is often slow, and the computational complexity is high

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