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

Indexed by:期刊论文

First Author:Zhang, Yi

Correspondence Author:Zhang, Y (reprint author), East China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China.

Co-author:Zhang, Liwei,Wu, Jia

Journal:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

Included Journals:SCIE

Volume:14

Issue:3

Page Number:981-1005

ISSN No.:1547-5816

Key Words:Mathematical program with symmetric cone complementarity constraints; C-stationary point; parametric smoothing approach; rate of convergence

Abstract: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.

Date of Publication:2018-07-01