GLOBAL AND GLOBAL LINEAR CONVERGENCE OF A SMOOTHING ALGORITHM FOR THE CARTESIAN P*(κ)-SCLCP

被引：7

作者：

Huang, Zheng-Hai ^{[1
]}

Lu, Nan ^{[2
]}

机构：

[1] Tianjin Univ, Sch Sci, Dept Math, Tianjin 300072, Peoples R China

[2] Xidian Univ, Dept Math, Xian 710071, Peoples R China

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2012年 / 8卷 / 01期

关键词：

Complementarity problem; symmetric cone; Euclidean Jordan algebra; smoothing algorithm; NONLINEAR COMPLEMENTARITY-PROBLEMS; INTERIOR CONTINUATION ALGORITHM; ONE-PARAMETRIC CLASS; QUADRATIC CONVERGENCE; NEWTON ALGORITHM; JORDAN ALGEBRAS; P-0;

D O I：

10.3934/jimo.2012.8.67

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we consider the linear complementarity problem over Euclidean Jordan algebras with a Cartesian P-*(K)-transformation, which is denoted by the Cartesian P-*(K)-SCLCP. A smoothing algorithm is extended to solve the Cartesian P, (K)-SCLCP. We show that the algorithm is globally convergent if the problem concerned has a solution. In particular, we show that the algorithm is globally linearly convergent under a weak assumption.

引用

页码：67 / 86

页数：20

共 50 条

[31] A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian P0-property
Liu, Xiangjing
Liu, Sanyang
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2020, 92 (02) : 229 - 247
[32] A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones
Xiao-Hong Liu
Zheng-Hai Huang
Mathematical Methods of Operations Research, 2009, 70 : 385 - 404
[33] The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem
Tang J.
Dong L.
Fang L.
Zhou J.
Tang, J. (jingyongtang@163.com), 1600, Springer Verlag (43): : 307 - 328
[34] A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems
Lu, Nan
Huang, Zheng-Hai
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2014, 161 (02) : 446 - 464
[35] A global and local superlinear continuation-smoothing method for P0 and R0 NCP or monotone NCP
Chen, BT
Chen, XJ
SIAM JOURNAL ON OPTIMIZATION, 1999, 9 (03) : 624 - 645
[36] On the P*(κ) horizontal linear complementarity problems over Cartesian product of symmetric cones
Asadi, S.
Mansouri, H.
Darvay, Zs.
Zangiabadi, M.
OPTIMIZATION METHODS & SOFTWARE, 2016, 31 (02) : 233 - 257
[37] On smoothing methods for the P0 matrix linear complementarity problem
Chen, XJ
Ye, YY
SIAM JOURNAL ON OPTIMIZATION, 2000, 11 (02) : 341 - 363
[38] A Corrector-Predictor Interior-Point Algorithm for P()-HLCPs Over Cartesian Product of Symmetric Cones
Asadi, S.
Zangiabadi, M.
Mansouri, H.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (01) : 20 - 38
[39] Some global uniqueness and solvability results for linear complementarity problems over symmetric cones
Gowda, M. Seetharama
Sznajder, R.
SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (02) : 461 - 481
[40] A Smoothing Algorithm with Constant Learning Rate for Training Two Kinds of Fuzzy Neural Networks and Its Convergence
Li, Long
Qiao, Zhijun
Long, Zuqiang
NEURAL PROCESSING LETTERS, 2020, 51 (02) : 1093 - 1109

← 1 2 3 4 5 →