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论文类型：期刊论文
发表时间：2018-07-01
发表刊物：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
收录刊物：SCIE
卷号：14
期号：3
页面范围：981-1005
ISSN号：1547-5816
关键字：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.