文献类型：期刊文献

英文题名：First order necessary optimality conditions for mathematical programs with second-order cone complementarity constraints

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

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

年份：2015

卷号：63

期号：2

起止页码：253

外文期刊名：JOURNAL OF GLOBAL OPTIMIZATION

收录：;EI(收录号：20151400711286);WOS:【SCI-EXPANDED(收录号:WOS:000361485700003)】；

基金：This work was supported by the National Natural Science Foundation of China under Projects No. 11401210, No. 11301049, No. 91130007, No. 91330206 and the Fundamental Research Funds for the Central Universities under Project No. 222201314037.

语种：英文

外文关键词：Mathematical program with second-order cone complementarity constraints; Necessary optimality conditions; S-,M-,C-,A-stationary points; Constraint qualifications

摘要：This paper is to develop first order necessary optimality conditions for a mathematical program with second-order cone complementarity constraints (MPSCC) which includes the mathematical program with (vector) complementarity constraints (MPCC) as a special case. Like the case of MPCC, Robinson's constraint qualification fails at every feasible point of MPSCC if we treat the MPSCC as an ordinary optimization problem. Using the formulas of regular and limiting coderivatives and generalized Clarke's Jacobian of the projection operator onto second-order cones from the literature, we present the S-, M-, C- and A-stationary conditions for a MPSCC problem. Moreover, several constraint qualifications including MPSCC-Abadie CQ, MPSCC-LICQ, MPSCC-MFCQ and MPSCC-GMFCQ are proposed, under which a local minimizer of MPSCC is shown to be a S-, M-, C- or A-stationary point.