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Differentiability properties of metric projections onto convex sets

Alexander Shapiro (ashapiro***at***isye.gatech.edu)

Abstract: It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems.

Keywords: Metric projection, directional differentiability, second order regularity, cone reducibility, nondegeneracy

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 11/14/2013
Entry Accepted: 11/14/2013
Entry Last Modified: 08/17/2014

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