Learning based convex approximation for constrained parametric optimization

TL;DR

This paper introduces a novel ICNN-based self-supervised learning framework for constrained optimization that guarantees feasibility, improves optimality, and converges reliably, outperforming existing methods on various benchmarks.

Contribution

The paper presents a new learning-based approach combining ICNNs with augmented Lagrangian methods, providing convergence guarantees and superior performance in constrained optimization tasks.

Findings

Achieves better optimality gap and convergence rate than state-of-the-art methods.

Ensures non-strict constraint feasibility throughout optimization.

Demonstrates superior accuracy and efficiency on benchmark problems.

Abstract

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism, our framework ensures \emph{non-strict constraint feasibility}, \emph{better optimality gap}, and \emph{best convergence rate} with respect to the state-of-the-art learning-based methods. We provide a rigorous convergence analysis, showing that the algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the original problem even when the internal solver is a neural network, and the approximation error is bounded. We test our approach on a range of benchmark tasks including quadratic programming (QP), nonconvex programming, and large-scale AC optimal power flow problems. The results demonstrate that compared to existing solvers (e.g., \texttt{OSQP}, \texttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.