Conditional Infimum and Hidden Convexity in Optimization
Optimization and Control
2021-04-13 v1
Abstract
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting hidden convexity. We develop the theory of the conditional infimum, and we establish a tower property, relevant for minimization problems. Thus equipped, we provide a sufficient condition for hidden convexity in nonconvex minimization problems. We illustrate our result on nonconvex quadratic minimization problems. We conclude with perspectives for using the conditional infimum in relation to the so-called S-procedure, to couplings and conjugacies, and to lower bound convex programs.
Cite
@article{arxiv.2104.05266,
title = {Conditional Infimum and Hidden Convexity in Optimization},
author = {Jean-Philippe Chancelier and Michel de Lara},
journal= {arXiv preprint arXiv:2104.05266},
year = {2021}
}