Nonlinear optimization via novel neural network methods

Abstract

This paper introduces a novel approach for solving high-dimensional nonlinear optimization problems by integrating neural networks into the optimization process. The method leverages the capabilities of neural networks to efficiently handle complex, high-dimensional data and to approximate discrete numerical solutions of nonlinear optimization problems using continuous functions. By combining the nonlinear mapping ability of neural networks with iterative optimization algorithms, the proposed approach provides a superior method to solve nonlinear optimization problems. The paper demonstrates the adaptability of neural network-based solution methods in solving various nonlinear optimization problems and illustrates that the method can be applied to many different problem scenarios. The effectiveness and correctness of the proposed method are demonstrated through examples.