Some dual conditions for global weak sharp minimality of nonconvex functions

TL;DR

This paper develops dual conditions for establishing global weak sharp minimality in nonconvex functions, extending convex case results without requiring the Asplund property, using quasidifferential calculus.

Contribution

It introduces novel dual conditions for weak sharp minimality in nonconvex functions, broadening applicability beyond convex functions and removing the need for Asplund space assumptions.

Findings

Provides sufficient conditions for global weak sharp minimality in nonconvex functions.

Extends convex weak sharp minimality conditions to nonconvex settings.

Avoids the need for Asplund property in the underlying space.

Abstract

Weak sharp minimality is a notion emerged in optimization, whose utility is largeley recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behaviour of such problems. In the present paper some dual constructions of nonsmooth analysis, mainly related to quasidifferential calculus and its recent developments, are employed in formulating sufficient conditions for global weak sharp minimality. They extend to nonconvex functions a condition, which is known to be valid in the convex case. A feature distinguishing the results here proposed is that they avoid to assume the Asplund property on the underlying space.