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对称锥互补问题的一个惩罚NR函数(英文) 被引量：4

A Penalized NR Function for Symmetric Cone Complementarity Problems
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摘要 本文建立了一个对称锥互补问题的惩罚自然剩余函数,并且证明了单调情形下其相应势函数的水平有界性. In this paper,we establish a penalized natural residual function for symmetric cone complementarity problems,and show the level-boundedness of the merit function related to the natural residual function for the SCCP with monotonicity.
作者 孔令臣 修乃华 秦林霞
机构地区 北京交通大学应用数学系
出处 《数学进展》 CSCD 北大核心 2011年第2期173-178,共6页 Advances in Mathematics（China）
基金 supported by NSFC(No.10831006) the National Basic Research Program of China(No.2010CB732501)
关键词 对称锥互补问题 水平有界性 自然剩余函数 symmetric cone complementarity problem level-boundedness natural residual function
分类号 O224 [理学—运筹学与控制论]
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参考文献15

  • 1Chen X.D., Sun D. and Sun J., Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems, Comput. Optim. Appl., 2003, 25: 39- 56.
  • 2Facchinei, F. and Pang J.-S., Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I and II, New York: Springer-Verlag, 2003.
  • 3Faraut, J. and Koranyi, A., Analysis on Symmetric Cones, New York: Oxford University Press, 1994.
  • 4Faybusovich, L., Euclidean Jordan algebras and interior-point algorithms, Positivity, 1997, 1: 331-357.
  • 5Gowda, M.S., Sznajder, R. and Tao J., Some P-properties for linear transformations on Euclidean Jordan algebras, Linear Algebra and Its Applications, 2004, 393: 203-232.
  • 6Gowda, M.S. and Sznajder, R., Automorphism invariance of P and GUS properties of linear transforma- tions on Euclidean Jordan algebras, Math. Oper. Res., 2006, 31: 109-123.
  • 7Koecher, M., The Minnesota Notes on Jordan Algebras and Their Applications, edited and annotated by A. Brieg and S. Walcher, Berlin: Springer, 1999.
  • 8Kong L.C. and Xiu N.H., New smooth C-functions for symmetric cone complementarity problems, Optimization Letters, 2007, 1: 391-400.
  • 9Kong L.C., Sun J. and Xiu N.H., A regularized smoothing Newton method for symmetric cone comple- mentarity problems, SIAM Journal on Optimization, 2008, 19: 1028-1047.
  • 10Liu Y., Zhang L. and Wang Y., Some properties of a class of merit functions for symmetric cone comple- mentarity problems, Asia-Pacific Journal of Operational Research, 2006, 23: 473-496.

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数学进展
2011年 第2期

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