Parametric Nonconvex Optimization via Convex Surrogates

TL;DR

This paper introduces a learning-based method to create convex surrogate problems for parametric nonconvex optimization, enabling efficient solutions via parallel convex optimization, demonstrated through path tracking experiments.

Contribution

It proposes a novel surrogate construction method for nonconvex problems using convex compositions, facilitating direct convex optimization solutions.

Findings

Surrogate problems closely approximate original nonconvex problems.

The method enables solving complex nonconvex problems efficiently.

Numerical experiments validate the approximation quality.

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.