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一类非对称单调变分不等式的交替方向法 被引量:3

An Alternating Direction Method for Solving a Class of Asymmetric Variational Inequalities
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摘要 对一类非对称变分不等式问题提出了交替方向法,推广了交替方向仅适用于等式约束或不等约束的情形,得出了迭代序列的一些性质及收敛性. In this paper,an alternating direction method is studied for solving a class of asymmetric monotone variational inequalities subject to equalities and inequalities. Some properties of the iterative sequence and convergence properties are derived.
作者 胡伯霞
出处 《数学理论与应用》 2005年第3期42-44,共3页 Mathematical Theory and Applications
关键词 变分不等式 交替方向法 收敛性 单调变分不等式 非对称 变分不等式问题 等式约束 迭代序列 variational inequality alternating direction method convergence property
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参考文献1

  • 1Patrick T. Harker,Jong-Shi Pang. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications[J] 1990,Mathematical Programming(1-3):161~220

同被引文献17

  • 1胡伯霞.非对称变分不等式的另一类非精确交替方向法[J].衡阳师范学院学报,2005,26(3):23-25. 被引量:2
  • 2周叔子,胡伯霞.一类非对称变分不等式的非精确交替方向法[J].湖南大学学报(自然科学版),2007,34(4):78-80. 被引量:3
  • 3H. Uzawa. Iterative Methods for Concave Programming[A].K.J. Arrow, L. Hurwicz, H. Uzawa. Studies in Linear and Nonlinear Programnfing[C].Stanford:Stanford University Press,1958.
  • 4D. Gabay.Applications of the Method of Multipliers to Variational Inequalities[A].M. Fortin, R. Glowinski. Augmented Lagrangian Methods:Applications to the Solution of Boundary-Valued Problems[C].North-Holland:Amsterdam Press,1983.
  • 5D. Gabay, B. Mercier.A Dual Algorithm for the Solution of Nonlinear Variational Problems Via Finite-Element Approximations[J]. Computers and Mathematics with Applications,1976,2(1).
  • 6B.S. He, J. Zhou.A Modified Ahemating Direction Method for Convex Minimization Problems[J].Applied Mathematics Letter,2000, (13).
  • 7D.R. Hart, H.K. Lo. A New Stepsize Rule in He and Zhou's Alternating Direction Method[J].Applied Mathematics Letters,2002,15.
  • 8D.R.Han, H.K.Lo. New Alternating Direction Method for a Class of Nonlinear Variational Inequality Problems[J].Joumal of Optinfization Theory and Applications,2002,112(3 ).
  • 9D.R. Han. A Modified Alternating Direction Method for Variational Inequality Problems[J].Applied Mathematics and Optimization, 2002,(45).
  • 10Z.Zhou,A.Chen,D.R.Han. An Extended Alternating Direction Method for Variational Inequality Problems with Linear Equality and Inequality Constraints[J].Applied Mathematics and Computation,2007, (184).

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