Learning based convex approximation for constrained parametric optimization

2025-05-07

AI Summary

This work addresses continuous constrained optimization problems by proposing a self-supervised learning framework based on Input-Convex Neural Networks (ICNNs), integrating the Augmented Lagrangian Method (ALM) with an explicit constraint correction mechanism. The method embeds a solver structure within the neural network and—uniquely among learned solvers—provides the first rigorous proof of convergence to Karush–Kuhn–Tucker (KKT) points of the original problem, balancing near-feasibility with theoretical convergence guarantees. Evaluated on quadratic programming, nonconvex programming, and large-scale AC optimal power flow tasks, the approach significantly outperforms state-of-the-art solvers—including OSQP, IPOPT, DC3, and PDL—in feasibility, optimality gap, and convergence speed. It achieves superior trade-offs across solution accuracy, constraint satisfaction, and computational efficiency.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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., exttt{OSQP}, exttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.

Problem

• Solves continuous constrained optimization problems using ICNN
• Ensures non-strict feasibility and better optimality gap
• Achieves superior accuracy, feasibility, and computational efficiency

Innovation

• Input convex neural network for optimization
• Augmented Lagrangian with constraint correction
• Convergence to KKT point guaranteed