A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone

被引：6
作者：
Cruz, J. Y. Bello [1 ]
Ferreira, O. P. [2 ]
Nemeth, S. Z. [3 ]
Prudente, L. F. [2 ]
机构：
[1] Northern Illinois Univ, Dept Math Sci, WH 366, De Kalb, IL 60115 USA
[2] Univ Fed Goias, IME, Ave Esperanga S-N,Campus Samambaia, BR-74690900 Goiania, Go, Brazil
[3] Univ Birmingham, Sch Math, Watson Bldg, Birmingham B15 2TT, W Midlands, England
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2017年 / 513卷
关键词：
Semi-smooth system; Conic programming; Second order cone; Semi-smooth Newton method; ABSOLUTE VALUE EQUATIONS; ITERATIVE SOLUTION; GAME-THEORY; SYSTEMS; REFORMULATION; CONVERGENCE;
D O I：
10.1016/j.laa.2016.10.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is globally and Q-linearly convergent to a solution. As an application, the obtained results are used to study the linear second order cone complementarity problem, with special emphasis on the particular case of positive definite matrices. Moreover, some computational experiments designed to investigate the practical viability of the method are presented. (C) 2016 Published by Elsevier Inc.
引用
收藏
页码：160 / 181
页数：22
相关论文
共 35 条
  • [1] Robust game theory
    Aghassi, M
    Bertsimas, D
    [J]. MATHEMATICAL PROGRAMMING, 2006, 107 (1-2) : 231 - 273
  • [2] Box-constrained minimization reformulations of complementarity problems in second-order cones
    Andreani, R.
    Friedlander, A.
    Mello, M. P.
    Santos, S. A.
    [J]. JOURNAL OF GLOBAL OPTIMIZATION, 2008, 40 (04) : 505 - 527
  • [3] [Anonymous], 1990, CLASSICS APPL MATH
  • [4] [Anonymous], 1965, The algebraic eigenvalue problem
  • [5] A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming
    Barrios, J. G.
    Bello Cruz, J. Y.
    Ferreira, O. P.
    Nemeth, S. Z.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 301 : 91 - 100
  • [6] Projection onto simplicial cones by Picard's method
    Barrios, Jorge
    Ferreira, Orizon P.
    Nemeth, Sandor Z.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 480 : 27 - 43
  • [7] On the global convergence of the inexact semi-smooth Newton method for absolute value equation
    Bello Cruz, J. Y.
    Ferreira, O. P.
    Prudente, L. F.
    [J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2016, 65 (01) : 93 - 108
  • [8] ITERATIVE SOLUTION OF PIECEWISE LINEAR SYSTEMS
    Brugnano, Luigi
    Casulli, Vincenzo
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2008, 30 (01) : 463 - 472
  • [9] ITERATIVE SOLUTION OF PIECEWISE LINEAR SYSTEMS AND APPLICATIONS TO FLOWS IN POROUS MEDIA
    Brugnano, Luigi
    Casulli, Vincenzo
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2009, 31 (03) : 1858 - 1873
  • [10] Iterative solutions of mildly nonlinear systems
    Casulli, Vincenzo
    Zanolli, Paola
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (16) : 3937 - 3947
1234