Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

TL;DR

This paper establishes conditions for weak sharp minima at infinity in nonsmooth optimization and explores their implications for solution stability under linear perturbations, with applications to quasiconvex functions.

Contribution

It introduces new sufficient conditions for weak sharp minima at infinity and links these to solution stability in nonconvex optimization problems.

Findings

Conditions for weak sharp minima at infinity are derived.

These conditions help analyze solution stability under perturbations.

Applications include a subclass of quasiconvex functions stable under linear additivity.

Abstract

We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.