Mordukhovich Derivatives and Covering Constant for Set-Valued Metric Projection in General Banach Spaces

Abstract

In this paper, we find the explicit representation of the set-valued metric projection operator from l1 to the unit closed ball in l1. By using this representation, we investigate the properties of the Mordukhovich derivatives of the set-valued metric projection operator, which is applied to calculate its covering constant. As a special case, we consider the 2-d Banach space. We find the explicit solutions of the set-valued metric projection operator from the considered 2-d Banach space to its unit closed ball. By these solutions, we will calculate its Mordukhovich derivatives in details.