Strong Stationarity for Optimization Problems with Complementarity Constraints in Absence of Polyhedricity

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• 作者：Gerd Wachsmuth
• 关键词：Mathematical programs with complementarity constraints ; Strong stationarity ; Conic programming ; Semidefinite cone ; Second ; order cone ; Polyhedricity
• 刊名：Set-Valued and Variational Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：25
• 期：1
• 页码：133-175
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Probability Theory and Stochastic Processes;
• 出版者：Springer Netherlands
• ISSN：1877-0541
• 卷排序：25

文摘

We consider mathematical programs with complementarity constraints in Banach spaces. In particular, we focus on the situation that the complementarity constraint is defined by a non-polyhedric cone K. We demonstrate how strong stationarity conditions can be obtained in an abstract setting. These conditions and their verification can be made more precise in the case that Z is a Hilbert space and if the projection onto K is directionally differentiable with a derivative as given in Haraux (Journal of the Mathematical Society of Japan 29(4), 615–631, 1977, Theorem 1). Finally, we apply the theory to optimization problems with semidefinite and second-order-cone complementarity constraints. We obtain that local minimizers are strongly stationary under a variant of the linear-independence constraint qualification, and these are novel results.