Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems

被引：0
作者：
L.R. Huang
K. F. Ng
机构：
[1] South China Normal University,Professor, Department of Mathematics
[2] Chinese University of Hong Kong,Professor, Department of Mathematics
来源：
Journal of Optimization Theory and Applications | 2005年 / 125卷
关键词：
Variational inequality problems; descent methods; optimization problems; error bounds;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We investigate whether some merit functions for variational inequality problems (VIP) provide error bounds for the underlying VIP. Under the condition that the involved mapping F is strongly monotone, but not necessarily Lipschitz continuous, we prove that the so-called regularized gap function provides an error bound for the underlying VIP. We give also an example showing that the so-called D-gap function might not provide error bounds for a strongly monotone VIP.
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页码：299 / 314
页数：15
相关论文
共 16 条
  • [1] Fukushima M.(1992)Equivalent Differentiable Optimization Problems and Descent Methods for Asymmetric Variational Inequality Problems Mathematical Programming 53 99-110
  • [2] Wu. J.H.(1993)A General Descent Framework for the Monotone Variational Inequality Problem. Mathematical Programming 61 281-300
  • [3] Florian. M.(1997)Unconstrained Optimization Reformulations of Variational Inequality Problems Journal of Optimization Theory and Applications 92 439-456
  • [4] Marcotte P.(1997)Equivalence of Variational Inequality Problems to Unconstrained Optimization. Mathematical Programming 78 347-355
  • [5] Yamashita. N.(1997)Equivalent Unconstrained Minimization and Global Error Bounds for Variational Inequality Problems SIAM Journal on Control and Optimization 35 273-284
  • [6] Taji. K.(1999)Exceptional Families and Existence Theorems for Variational Inequality Problems Journal of Optimization Theory and Application 2 475-495
  • [7] Fukushima. M.(2001)Error Bounds for Lower Semicontinuous Functions in Normed Spaces SIAM Journal on Optimization 12 1-17
  • [8] Peng J.M.(1989)Variational Principles for Variational Inequalities Numerical Functional Analysis and Optimization 10 863-874
  • [9] Yamashita N.(undefined)undefined undefined undefined undefined-undefined
  • [10] Fukushima M.(undefined)undefined undefined undefined undefined-undefined
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