A smoothing Newton method for symmetric cone complementarity problem

被引：6
作者：
Liu L. [1 ]
Liu S. [1 ]
Wu Y. [1 ]
机构：
[1] Department of Mathematics and Statistics, Xidian University, Xi’an
来源：
J. Appl. Math. Comp. | / 1-2卷 / 175-191期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Cartesian P[!sub]0[!/sub]-property; Coerciveness; Complementarity problem; Smoothing Newton method; Symmetric cone;
D O I：
10.1007/s12190-014-0768-3
中图分类号：
学科分类号：
摘要：
We first extend a new class of smoothing functions, which contains the well-known Chen-Harker-Kanzow-Smale smoothing function and Huang-Han-Chen smoothing function as special cases, for the nonlinear complementarity problem to the symmetric cone complementarity problem (SCCP). And then we present a smoothing Newton algorithm for the SCCP based on the new class of smoothing functions. Both the existence of Newton directions and the boundedness of the level set are showed for the SCCP with the Cartesian P0-property, which contains the monotone SCCP as a special case. The global linear convergence and locally superlinear convergence are established under a nonsingular assumption. Some numerical results for second order cone complementarity problems, a special case of SCCP, show that the proposed algorithm is effective. © 2014, Korean Society for Computational and Applied Mathematics.
引用
收藏
页码：175 / 191
页数：16
相关论文
共 32 条
  • [1] Che H.T., Wang Y.J., Li M.X., A smoothing inexact Newton method for (Formula Presented.) nonlinear complementarity problem, Front. Math. China, 7, pp. 1043-1058, (2012)
  • [2] Chen X.D., Sun D., Sun J., Complementarity functions and numerical experiments on smoothing Newton methods for second-order-cone complementarity problems, Comput. Optim. Appl., 25, pp. 39-56, (2003)
  • [3] Chen X., Qi H.D., Cartesian P-property and its applications to the semidefinite linear complementarity problem, Math. Program. Ser. A, 106, pp. 177-201, (2006)
  • [4] Chua C.B., Yi P., A continuation method for nonlinear complementarity problems over symmetric cones, SIAM J. Optim., 20, pp. 2560-2583, (2010)
  • [5] Chua C.B., Lin H.L., and Yi, P., (2009)
  • [6] Clarke F.H., Optimization and nonsmooth analysis, (1983)
  • [7] Facchinei F., Pang F., Finite dimensional variational ineqaulities and complementarity problems, vol I and II, (2003)
  • [8] Faraut J., Koranyi A., Analysis on symmetric cones, (1994)
  • [9] Gowda M.S., Sznajder R., Tao J., Some P-properties for linear transformations on Euclidean Jordan algebras, Linear Algebr. Appl., 393, pp. 203-232, (2004)
  • [10] Hayashi S., Yamashita N., Fukushima M., A combined smoothing and regularization method for monotone second-order cone complementarity problems, SIAM J. Optim., 15, pp. 593-615, (2005)
1234