A combined smoothing and regularization method for monotone second-order cone complementarity problems

被引：190

作者：

Hayashi, S ^{[1
]}

Yamashita, N ^{[1
]}

Fukushima, M ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Kyoto 6068501, Japan

来源：

SIAM JOURNAL ON OPTIMIZATION | 2005年 / 15卷 / 02期

关键词：

second-order cone; complementarity problem; smoothing method; regularization method;

D O I：

10.1137/S1052623403421516

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The second-order cone complementarity problem (SOCCP) is a wide class of problems containing the nonlinear complementarity problem (NCP) and the second-order cone programming problem (SOCP). Recently, Fukushima, Luo, and Tseng [SIAM J. Optim., 12 ( 2001), pp. 436-460] extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas for the Jacobians of the smoothing functions and gave conditions for the Jacobians to be invertible. In this paper, we propose a globally and quadratically convergent algorithm, which is based on smoothing and regularization methods, for solving monotone SOCCP. In particular, we study strong semismoothness and Jacobian consistency, which play an important role in establishing quadratic convergence of the algorithm. Furthermore, we examine the effectiveness of the algorithm by means of numerical experiments.

引用

页码：593 / 615

页数：23

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