Generic nondegeneracy in convex optimization

TL;DR

This paper proves that for convex functions, minimizers are typically nondegenerate when subjected to almost all linear perturbations, extending to lower-C^2 functions.

Contribution

It establishes a generic nondegeneracy result for convex and lower-C^2 functions under linear perturbations, broadening understanding of solution stability.

Findings

Minimizers of convex functions are nondegenerate under almost all linear perturbations.

The nondegeneracy result extends to lower-C^2 functions.

Provides theoretical foundation for stability analysis in convex optimization.

Abstract

We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally, for lower-C^2 functions.