Differentiability Properties of Metric Projections onto Convex Sets

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• 作者：Alexander Shapiro
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：169
• 期：3
• 页码：953-964
• 全文大小：428 KB
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：169

文摘

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.KeywordsMetric projectionDirectional differentiabilitySecond-order regularityCone reducibilityNondegeneracy