The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem

被引：5

作者：

Tang J. ^{[1
]}

Dong L. ^{[1
]}

Fang L. ^{[2
]}

Zhou J. ^{[3
]}

机构：

[1] College of Mathematics and Information Science, Xinyang Normal University

[2] College of Mathematics and System Science, Taishan University

[3] Department of Mathematics, School of Science, Shandong University of Technology

来源：

Tang, J. (jingyongtang@163.com) | 1600年 / Springer Verlag卷 / 43期

基金：

中国国家自然科学基金;

关键词：

Convergence; Euclidean Jordan algebra; Smoothing function; Smoothing Newton method; Symmetric cone complementarity problem;

D O I：

10.1007/s12190-013-0665-1

中图分类号：

学科分类号：

摘要：

The symmetric cone complementarity problem (denoted by SCCP) is a broad class of optimization problems, which contains the semidefinite complementarity problem, the second-order cone complementarity problem, and the nonlinear complementarity problem. In this paper we first extend the smoothing function proposed by Huang et al. (Sci. China 44:1107-1114, 2001) for the nonlinear complementarity problem to the context of symmetric cones and show that it is coercive under suitable assumptions. Based on this smoothing function, a smoothing-type algorithm, which is a modified version of the Qi-Sun-Zhou method (Qi et al. in Math. Program. 87:1-35, 2000), is proposed for solving the SCCP. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results for some second-order cone complementarity problems are reported which indicate that the proposed algorithm is effective. © 2013 Korean Society for Computational and Applied Mathematics.

引用

页码：307 / 328

页数：21

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