Optimization-Informed Neural Networks
This addresses a longstanding problem in fields like economics and engineering by enabling CNLP solving using only deep learning infrastructure, though it appears incremental as it builds on neurodynamic optimization methods.
The authors tackled solving constrained nonlinear optimization problems (CNLPs) by proposing optimization-informed neural networks (OINN), which reformulate CNLPs as initial value problems and use neural networks as approximate solutions, achieving effectiveness on classical problems like variational inequalities and nonlinear complementary problems.
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.