New Approach to Solving a System of Variational Inequalities and Hierarchical Problems

被引：0
作者：
P. E. Maingé
机构：
[1] Université des Antilles-Guyane,GRIMAAG, Département Scientifique Interfacultaire
来源：
Journal of Optimization Theory and Applications | 2008年 / 138卷
关键词：
Fixed points; System of variational inequalities; Nash stationary points; Hierarchical problems; Subgradient projection;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper deals with a viscosity iterative method, in real Hilbert spaces, for solving a system of variational inequalities over the fixed-point sets of possibly discontinuous mappings. Under classical conditions, we prove a strong convergence theorem for our method. The proposed algorithm can be applied for instance to solving variational inequalities in some situations when the projection methods fail. Moreover, the techniques of analysis are novel and provide new tools in designing approximation schemes for combined and bilevel optimization problems.
引用
收藏
页码：459 / 477
页数：18
相关论文
共 39 条
  • [1] Bauschke H.H.(2001)A weak-to-strong convergence principle for Fejer monotone methods in Hilbert space Math. Oper. Res. 26 248-264
  • [2] Combettes P.L.(1997)Convex set theoretic image recovery by extrapolated iterations of paralell subgradients projections IEEE Trans. Image Process. 6 493-506
  • [3] Combettes P.L.(2004)Image restoration subject to a total variation constraint IEEE Trans. Image Process. 13 1213-1222
  • [4] Combetes P.L.(2004)Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings Numer. Funct. Anal. Optim. 25 619-655
  • [5] Pesquet J.C.(2005)Proximest Point and Steepest descent algorithm controlled by a slowly vanishing term. Applications to hierarchical minimization SIAM J. Optim. 2 555-572
  • [6] Yamada I.(1998)Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings Numer. Funct. Anal. Optim. 19 33-55
  • [7] Ogura N.(2007)Strong convergence of an iterative method for hierarchical fixed point problems Pac. J. Optim. 3 529-538
  • [8] Cabot A.(2007)An explicit descent method for bilevel convex optimization J. Convex Anal. 14 227-238
  • [9] Deutsch F.(2003)Convergence of Hybrid steepest descent methods for variational inequalities J. Optim. Theory Appl. 119 185-201
  • [10] Yamada I.(2007)Convergence analysis of modified hybrid steepest descent methods with variable parameters for variational inequalities J. Optim. Theory Appl. 132 51-69
1234