The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems

被引：0
作者：
Yi-Fen Ke
Chang-Feng Ma
Huai Zhang
机构：
[1] University of Chinese Academy of Sciences,Key Laboratory of Computational Geodynamics
[2] Fujian Normal University,College of Mathematics and Informatics and FJKLMAA
来源：
Numerical Algorithms | 2018年 / 79卷
关键词：
Second-order cone; Linear complementarity problem; Jordan algebra; Matrix splitting; Iteration method; 90C33; 65H10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For the second-order cone linear complementarity problems, abbreviated as SOCLCPs, we establish two classes of modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently the SOCLCP as an implicit fixed-point equation based on Jordan algebra associated with the second-order cone. The convergence of these modulus-based matrix splitting iteration methods has been established and the optimal iteration parameters of these methods are discussed when the splitting matrix is symmetric positive definite. Numerical experiments have shown that the modulus-based iteration methods are effective for solving the SOCLCPs.
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页码：1283 / 1303
页数：20
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共 89 条
  • [21] Pan S(2005)A matrix-splitting method for symmetric affine second-order cone complementarity problems J. Comput. Appl. Math. 175 335-353
  • [22] Fukushima M(2014)An efficient matrix splitting method for the second-order cone complementarity problem SIAM J. Optim. 24 1178-1205
  • [23] Luo Z-Q(2005)On Q and R0 properties of a quadratic representation in linear complementarity problems over the second-order cone Linear Algebra Appl. 397 85-97
  • [24] Tseng P(2003)Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems Math. Oper. Res. 28 39-63
  • [25] Hayashi S(2006)Automorphism invariance of P- and GUS-properties of linear transformations on Euclidean Jordan algebras Math. Oper. Res. 31 109-123
  • [26] Yamashita N(2007)Some global uniqueness and solvability results for linear complementarity problems over symmetric cones SIAM J. Optim. 18 461-481
  • [27] Fukushima M(2010)Modulus-based matrix splitting iteration methods for linear complementarity problems Numer. Linear Algebra Appl. 17 917-933
  • [28] Chen X-D(2004)Some P-properties for linear transformations on Euclidean Jordan algebras Linear Algebra Appl. 393 203-232
  • [29] Sun D(2013)The GUS-property of second-order cone linear complementarity problems Math. Program. 141 295-317
  • [30] Sun J(2014)On the convergence analysis of two-step modulus-based matrix splitting iteration method for linear complementarity problems Appl. Math. Comput. 243 413-418
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