Some Dual Conditions for Global Weak Sharp Minimality of Nonconvex Functions

Abstract

Weak sharp minimality is a notion emerged in optimization whose utility is largely recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behavior of such problems. In this article, 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.