On invex functions with same {\eta} in single and multivalued nonsmooth optimization with Clarke's subdifferential

TL;DR

This paper characterizes a finite family of nonsmooth invex functions with respect to the same function eta, using scalarization, to deepen understanding of their structure in nonsmooth optimization.

Contribution

It introduces a characterization of nonsmooth invex functions sharing the same eta through scalarized forms, advancing the theoretical framework of nonsmooth optimization.

Findings

Characterization of nonsmooth invex functions via scalarization.

Extension of invexity concepts to multivalued nonsmooth functions.

Theoretical insights into Clarke's subdifferential for these functions.

Abstract

In this paper, a finite family of nonsmooth locally Lipschitz continuous functions that are invex with respect to the same function {\eta} are characterized in terms of their scalarized counterparts.