文献类型：期刊文献

英文题名：ON THE CONVERGENCE PROPERTIES OF A SMOOTHING APPROACH FOR MATHEMATICAL PROGRAMS WITH SYMMETRIC CONE COMPLEMENTARITY CONSTRAINTS

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

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

年份：2018

卷号：14

期号：3

起止页码：981

外文期刊名：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000438848400009)】；

基金：This study is supported by the National Natural Science Foundation of China under projects No. 11401210, No. 11671183, No. 11571059, No. 91330206 and No. 11301049.

语种：英文

外文关键词：Mathematical program with symmetric cone complementarity constraints; C-stationary point; parametric smoothing approach; rate of convergence

摘要：This paper focuses on a class of mathematical programs with symmetric cone complementarity constraints (SCMPCC). The explicit expression of C-stationary condition and SCMPCC-linear independence constraint qualification (denoted by SCMPCC-LICQ) for SCMPCC are first presented. We analyze a parametric smoothing approach for solving this program in which SCMPCC is replaced by a smoothing problem P-epsilon depending on a (small) parameter epsilon. We are interested in the convergence behavior of the feasible set, stationary points, solution mapping and optimal value function of problem P-epsilon when epsilon -> 0 under SCMPCC-LICQ. In particular, it is shown that the convergence rate of Hausdorff distance between feasible sets F-epsilon and F is of order O(vertical bar epsilon vertical bar) and the solution mapping and optimal value of P-epsilon are outer semi-continuous and locally Lipschitz continuous at epsilon = 0 respectively. Moreover, any accumulation point of stationary points of P-epsilon is a C-stationary point of SCMPCC under SCMPCC-LICQ.