辽宁石油化工大学学报

辽宁石油化工大学学报 ›› 2005, Vol. 25 ›› Issue (2): 95-98.

• 基础学科 • 上一篇    

解变分不等式的广义拟牛顿法

田秋菊, 宋岱才   

  1. 辽宁石油化工大学理学院, 辽宁抚顺113001
  • 收稿日期:2004-10-28 出版日期:2005-06-20 发布日期:2017-04-18
  • 作者简介:田秋菊(1978 -), 女, 辽宁沈阳市, 在读硕士。

A Generalized New ton -Like Method fo r Solving Variational Inequalities

  1. School of Science , Liaoning University of Petroleum & Chemical Technology ,
    Fushun Liaoning 113001, P .R .China
  • Received:2004-10-28 Published:2005-06-20 Online:2017-04-18

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摘要： 　     变分不等式问题(记为VIP(X, F))就是求一个x ∈ X Rn , 使得F(x)T(y -x)≥0 , y ∈ X Rn 。将VIP(X, F)转化为混合非线性互补问题, 提出了一种解变分不等式的拟牛顿法。若ω＊是VIP(X, F)的解, H＊0={ h(x ＊), gi(x ＊);i ∈ B(x ＊)}列满秩, Q(ω＊)+H＊H＊T 是正定矩阵, Ti(ω), i =1 , 2 , 4 连续可微, T′i(ω), i=1, 2, 4 在点ω＊的邻域N(ω＊ , δ)内满足李普希兹条件, 那么由算法确定的序列{ωk}Q-二次收敛到VIP(X , F)的解ω＊ 。并在没有严格互补松弛性条件下证明了Q-超线性收敛

关键词: 变分不等式, 　广义拟牛顿法, 　Q-二次收敛性

Abstract:

　The variational inequality problem , denoted by VIP(X , F), is to find a vector x ∈ X  ∈ Rn to make F(x)T(y -x)≥0,y ∈ X ∈Rn .The problem VIP(X, F)can be reformulated as a mixed nonlinear complementarity problem .A generalized Newton-like method for solving variational inequalities was presented .If (ω＊)is a solution of VIP(X, F), H＊0 ={ h(x ＊), gi(x ＊); i ∈ B(x ＊)} is of full column rank and Q(ω＊)+H＊ H＊T is apositivedefinite matrix .Ti (ω), i =1 , 2, 4 are continuously differentiable , T′i(ω), i =1 , 2, 4, satisfy Lipschitz' s condition in the neighbourhood N(ω＊, δ), then the sequences{ωk}, generated by algorithm , converges Q -quadratically to VIP(X, F)' s solution ω＊, and prove Q -superlinear convergence without the strict complementarity slackness condition.

Key words: 　Variational inequality , Generalized New to n-like method , Q -quadratic conv ergence

引用本文

田秋菊, 宋岱才. 解变分不等式的广义拟牛顿法[J]. 辽宁石油化工大学学报, 2005, 25(2): 95-98.

TIAN Qiu -ju,SONG Dai -cai. A Generalized New ton -Like Method fo r Solving Variational Inequalities[J]. Journal of Liaoning Petrochemical University, 2005, 25(2): 95-98.

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