Interior point methods for equilibrium problems

被引:0
作者
Nils Langenberg
机构
[1] University of Trier,Department of Mathematics
来源
Computational Optimization and Applications | 2012年 / 53卷
关键词
Equilibrium problems; Fixed point problems; Bregman distances; Proximal-like methods; Interior point effect;
D O I
暂无
中图分类号
学科分类号
摘要
In the present paper we discuss three methods for solving equilibrium-type fixed point problems. Concentrating on problems whose solutions possess some stability property, we establish convergence of these three proximal-like algorithms that promise a very high numerical tractability and efficiency. For example, due to the implemented application of zone coercive Bregman functions, all these methods allow to treat the generated subproblems as unconstrained and, partly, explicitly solvable ones.
引用
收藏
页码:453 / 483
页数:30
相关论文
共 54 条
[1]  
Auslender A.(1999)A logarithmic-quadratic proximal method for variational inequalities Comput. Optim. Appl. 12 31-40
[2]  
Teboulle M.(1994)From optimization and variational inequalities to equilibrium problems Math. Stud. 63 123-145
[3]  
Ben-Tiba S.(1998)A generalized proximal point algorithm for the variational inequality problem in Hilbert space SIAM J. Optim. 8 197-216
[4]  
Blum E.(2002)Nash equilibria, variational inequalities and dynamical systems J. Optim. Theory Appl. 114 491-506
[5]  
Oettli W.(1992)Proximal minimization algorithm with D-functions J. Optim. Theory Appl. 73 451-464
[6]  
Burachik R.S.(1998)An interior point method with Bregman functions for the variational inequality problem with paramonotone operators Math. Program. 81 373-400
[7]  
Iusem A.N.(1993)Convergence analysis of a proximal-like minimization algorithm using Bregman functions SIAM J. Optim. 3 538-543
[8]  
Cavazutti E.(1988)Auxiliary problem principle extended to variational inequalities J. Optim. Theory Appl. 59 325-333
[9]  
Pappalardo M.(1993)Nonlinear proximal point algorithms using Bregman functions, with application to convex programming Math. Oper. Res. 18 202-226
[10]  
Passacantando M.(2007)Generalized Nash equilibrium problems 4OR 5 173-210