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对称锥互补问题的一类价值函数及其性质 被引量：2

A Class of Merit Function and Its Related Properties for Symmetric Cone Complementarity Problems
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摘要 利用Euclidean-Jordan代数将非线性互补问题(NCP)的一类价值函数推广到对称锥互补问题(SCCP)上,并证明了SCCP等价于一个无约束光滑极小化问题,且给出了此类价值函数的两个例子.此外,研究了使得价值函数具有全局误差界的条件,并给出了使得价值函数水平集有界的一个较弱条件. A class of merit functions for describing the nonlinear complementarity problems （NCP） was extended to that for describing the symmetric cone complementarity （SCCP） problems by the tool of Euclidean-Jordan algebras. And then it was shown that the SCCP is equivalent to an unconstrained smooth minimization via this new merit function and two examples of the class of merit function are given. Moreover, the conditions under which the new merit function provides a global error bound were studied with a weak condition given under which the new merit function has bounded level sets.
作者 刘丽霞 刘三阳 侯兆阳
机构地区 西安电子科技大学应用数学系 长安大学理学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2009年第3期456-460,共5页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:60674108)
关键词 互补问题 对称锥 价值函数 Euclidean-Jordan代数 complementarity problems symmetric cone merit function Euclidean-Jordan algebra
分类号 O221 [理学—运筹学与控制论]
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参考文献12

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同被引文献21

  • 1Isac G.Leray-schauder Type Alternatives,Complementarity Problems and Variational Inequalities[M].Berlin:Springer,2006.
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  • 7LI Gong-nong.Analysis for a Homotopy Path of Complementarity Problems Based onμ-Exceptional Family[J].Applied Mathematics and Computation,2005,169(1):657-670.
  • 8Chen J S,Gao H T,PAN Shao-hua.An R-Linearly Convergent Derivative-Free Algorithm for Nonlinear Complementarity Problems Based on the Generalized Fisher-Buemeister Merit Function[J].Journal of Computational and Applied Mathematics,2009,232(2):455-471.
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  • 10ZHAO Yun-bin,Isac G.Quasi-P*-Maps,P(γ,α,β)-Maps,Exceptional Family of Elements,and Complementarity Problems[J].Journal of Optimization Theory and Applications,2000,105(1):213-231.

引证文献2

二级引证文献7

吉林大学学报（理学版）
2009年 第3期

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