Characterizations of Nonsmooth Robustly Quasiconvex Functions

TL;DR

This paper establishes criteria for identifying robust quasiconvexity in lower semicontinuous functions using Fréchet subdifferentials within Asplund spaces, advancing the theoretical understanding of nonsmooth analysis.

Contribution

It introduces new criteria for robust quasiconvexity based on Fréchet subdifferentials, specifically in the context of Asplund spaces, which was not previously explored.

Findings

Criteria for robust quasiconvexity established

Use of Fréchet subdifferentials in Asplund spaces demonstrated

Advances in nonsmooth analysis theory

Abstract

Two criteria for the robust quasiconvexity of lower semicontinuous functions are established in terms of Fr\'echet subdifferentials in Asplund spaces.