A smoothing Newton method for second-order cone optimization based on a new smoothing function

被引：18

作者：

Tang, Jingyong ^{[1
,2
]}

He, Guoping ^{[3
]}

Dong, Li ^{[2
]}

Fang, Liang ^{[4
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Informat Sci & Engn, Qingdao 266510, Peoples R China

[4] Taishan Univ, Coll Math & Syst Sci, Tai An 271021, Shandong, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 218卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Second-order cone optimization; Smoothing Newton method; Global convergence; Quadratic convergence; INTERIOR-POINT ALGORITHMS; NONLINEAR COMPLEMENTARITY-PROBLEMS; CONTINUATION METHOD; CONVERGENCE;

D O I：

10.1016/j.amc.2011.06.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new smoothing function is given in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1317 / 1329

页数：13

共 34 条

[1] Second-order cone programming
Alizadeh, F
Goldfarb, D
[J]. MATHEMATICAL PROGRAMMING, 2003, 95 (01) : 3 - 51
[2] Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions
Bai, Y. Q.
Wang, G. Q.
Roos, C.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (10) : 3584 - 3602
[3] A global linear and local quadratic noninterior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions
Chen, BT
Xiu, NH
[J]. SIAM JOURNAL ON OPTIMIZATION, 1999, 9 (03) : 605 - 623
[4] An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Chen, JS
Tseng, P
[J]. MATHEMATICAL PROGRAMMING, 2005, 104 (2-3) : 293 - 327
[5] A one-step smoothing Newton method for second-order cone programming
Chi, Xiaoni
Liu, Sanyang
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (01) : 114 - 123
[6] A non-interior continuation method for second-order cone programming
Chi, Xiaoni
Liu, Sanyang
[J]. OPTIMIZATION, 2009, 58 (08) : 965 - 979
[7] Clarke F.H, 1983, OPTIMIZATION NONSMOO
[8] An efficient support vector machine cone programming for learning method with second-order large-scale problems
Debnath, R
Muramatsu, M
Takahashi, H
[J]. APPLIED INTELLIGENCE, 2005, 23 (03) : 219 - 239
[9] A new smoothing Newton-type method for second-order cone programming problems
Fang, Liang
He, Guoping
Hu, Yunhong
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (03) : 1020 - 1029
[10] Faraut J., 1994, Oxford Mathematical Monographs

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