文献类型：期刊文献

英文题名：Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions

作者：Wu, Jia[1];Zhang, Liwei[1];Zhang, Yi[2]

机构：[1]Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China;[2]E China Univ Sci & Technol, Sch Sci, Dept Math, Shanghai 200237, Peoples R China

年份：2014

卷号：22

期号：1

起止页码：155

外文期刊名：SET-VALUED AND VARIATIONAL ANALYSIS

收录：;EI(收录号：20220811693157);WOS:【SCI-EXPANDED(收录号:WOS:000330977100007)】；

基金：The research is supported by the National Natural Science Foundation of China under project No. 11071029 and the Fundamental Research Funds for the Central Universities under projects No. DUT12RC(3)51 and No. 222201314037.

语种：英文

外文关键词：Mathematical program with semidefinite cone complementarity; constraints; B-stationary condition; Constraint qualifications; Second-order sufficient conditions

摘要：The tangent cone of gph plays an important role in developing necessary conditions for mathematical programs with semidefinite cone complementarity constraints. We demonstrate an elegant formula for the tangent cone of gph, based on which the Bouligand stationary point is characterized explicitly. The relationships among different stationary points under certain constraint qualifications are discussed. Then we propose a second order sufficient condition which can be weakened under the strict complementarity condition. Importantly, for the sake of algorithm design, under the assumption of strict complementarity condition, we give a nonsmooth equation reformulation of the stationary point, whose smoothing system is verified to be nonsingular at the stationary point under the proposed second order sufficient condition.