Linear Proxy Constraints for Non-Linear Optimization Bottlenecks
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Solution Overview
Problem
Constrained optimization problems with non-linear constraints are computationally intensive and time-consuming, making it impractical for modern portfolio management to determine globally optimal solutions within acceptable time frames.
Innovation Solution
Implementing a computer-implemented method that replaces non-linear constraints with linear proxy constraints, using a machine learning process to approximate the original constraints, allowing for iterative adjustments and faster convergence to a feasible solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If non-linear constraints are used in constrained optimization problems, then measurement precision and reliability are improved, but computing time and complexity increase significantly
Solution Approach 1:
The patent creates a simplified copy of the non-linear constraint system by replacing non-linear constraints with linear proxy constraints. This linear approximation serves as a computationally efficient substitute that maintains the essential optimization behavior while dramatically reducing solution time from minutes to seconds.
Solution Approach 2:
The patent transforms the mathematical parameters of the constraint system by converting non-linear constraint equations into linear forms. This parameter transformation allows the optimization problem to be solved using efficient linear programming techniques while maintaining sufficient accuracy for portfolio management applications.
2Measurement precision
If non-linear constraints are used in constrained optimization problems, then optimization accuracy is improved, but device complexity and computational resources increase
Solution Approach 1:
The patent creates a simplified copy of the non-linear constraint system by replacing non-linear constraints with linear proxy constraints. This linear approximation serves as a computationally efficient substitute that maintains the essential optimization behavior while dramatically reducing solution time from minutes to seconds.
Solution Approach 2:
The patent substitutes complex non-linear mathematical operations with simpler linear operations. By replacing the mechanical computation of non-linear constraints with linear proxy constraints, the system achieves the same optimization goal with significantly reduced computational complexity and faster processing.
3Measurement precision
If iterative adjustments are made to achieve convergence, then optimization accuracy is improved, but loss of time increases
Solution Approach 1:
The patent performs preliminary action by pre-defining linear proxy constraints that approximate the non-linear constraints before the optimization process begins. This upfront preparation eliminates the need for repeated iterative adjustments during optimization, as the linear constraints can be solved directly or with minimal iterations, significantly reducing the time required to achieve convergence.
Data Source
AI summary
A method includes receiving, by a server device, a plurality of input settings from a client device. In a tangible memory, the server device stores the plurality of input settings. The server device sets a linear proxy constraint based on the plurality of input settings to replace a non-linear constraint. The server device solves a system of equations to determine a feasible solution. The server device determines the feasible solution. Based on the determining the feasible solution, determining, by the server device, whether a current solution satisfies a convergence criterion. In response to determining the current solution satisfies the convergence criterion, the current solution is stored in the tangible memory by the server device. In response to determining the current solution does not satisfy the convergence criterion, the server device updates one or more of the input settings and solving the system of equations.