Parametric Nonconvex Optimization via Convex Surrogates

2026-04-07

AI Summary

This work addresses the challenge of efficiently solving parametric nonconvex optimization problems by proposing a learning-driven surrogate modeling approach. The method constructs a surrogate function expressed as the pointwise minimum of a finite set of convex and monotonic functions, thereby reformulating the original nonconvex problem into a collection of convex subproblems that can be solved in parallel. This approach achieves, for the first time, a structured convex approximation of nonconvex objectives, offering both high approximation accuracy and significantly improved computational efficiency. Numerical experiments on nonconvex path-following tasks demonstrate the superior performance of the proposed method in terms of both solution accuracy and computational speed.

Abstract

This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions, given by the composition of convex and monotonic terms, so that the surrogate problem can be solved directly through parallel convex optimization. As a proof of concept, numerical experiments on a nonconvex path tracking problem confirm the approximation quality of the proposed method.

Problem

• parametric optimization
• nonconvex optimization
• surrogate problem
• convex approximation

Innovation

• parametric nonconvex optimization
• convex surrogate
• parallel convex optimization
• monotonic composition
• learning-based approximation