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论文类型：期刊论文

发表时间：2015-10-01

发表刊物：JOURNAL OF GLOBAL OPTIMIZATION

收录刊物：SCIE、EI、Scopus

卷号：63

期号：2

页面范围：253-279

ISSN号：0925-5001

关键字：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.