# Conditional Infimum and Hidden Convexity in Optimization

arXiv: https://arxiv.org/abs/2104.05266 · HTML: https://mlsanity.com/paper/2104.05266/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Solving Hidden Monotone Variational Inequalities with Surrogate Losses](https://mlsanity.com/paper/2411.05228/) (2024)

## Abstract (arXiv)

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.