Optimization-Informed Neural Networks

TL;DR

This paper introduces optimization-informed neural networks (OINN), a deep learning framework that reformulates constrained nonlinear optimization problems as neural network training tasks, enabling solutions without traditional solvers.

Contribution

The paper presents a novel approach that transforms CNLPs into neural network training problems using neurodynamic methods, eliminating the need for standard optimization or numerical solvers.

Findings

Successfully applied to classical problems like variational inequalities

Achieves solutions using deep learning infrastructure only

Demonstrates effectiveness on standard CNLP benchmarks

Abstract

Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep learning approach to solve CNLPs. By neurodynamic optimization methods, a CNLP is first reformulated as an initial value problem (IVP) involving an ordinary differential equation (ODE) system. A neural network model is then used as an approximate solution for this IVP, with the endpoint being the prediction to the CNLP. We propose a novel training algorithm that directs the model to hold the best prediction during training. In a nutshell, OINN transforms a CNLP into a neural network training problem. By doing so, we can solve CNLPs based on deep learning infrastructure only, without using standard optimization solvers or numerical integration solvers. The effectiveness of the proposed approach is demonstrated through a collection of classical problems, e.g., variational inequalities, nonlinear complementary problems, and standard CNLPs.