An extragradient algorithm for solving bilevel pseudomonotone variational inequalities

We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained.

[1]  Zhi-Quan Luo,et al.  Mathematical Programs with Equilibrium Constraints: Bibliography , 1996 .

[2]  T. D. Quoc,et al.  Extragradient algorithms extended to equilibrium problems , 2008 .

[3]  M. H. Xu,et al.  Neural networks for a class of bi-level variational inequalities , 2009, J. Glob. Optim..

[4]  Mikhail Solodov,et al.  An Explicit Descent Method for Bilevel Convex Optimization , 2006 .

[5]  Hans-Jakob Lüthi,et al.  On the Solution of Variational Inequalities by the Ellipsoid Method , 1985, Math. Oper. Res..

[6]  Tomonari Suzuki.  Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals , 2005 .

[7]  C. Baiocchi,et al.  Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .

[8]  I. Konnov,et al.  Descent methods for monotone equilibrium problems in Banach spaces , 2006 .

[9]  J. Strodiot,et al.  GENERALIZED PROJECTION METHOD FOR NON-LIPSCHITZ MULTIVALUED MONOTONE VARIATIONAL INEQUALITIES , 2009 .

[10]  Muhammad Aslam Noor,et al.  A new hybrid iterative algorithm for variational inequalities , 2010, Appl. Math. Comput..

[11]  I. Konnov.  Combined Relaxation Methods for Variational Inequalities , 2000 .

[12]  Le Dung Muu,et al.  Dual extragradient algorithms extended to equilibrium problems , 2011, Journal of Global Optimization.

[13]  Ali J. Chamkha,et al.  MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption , 2009 .

[14]  A. Bakushinskii,et al.  Ill-Posed Problems: Theory and Applications , 1994 .

[15]  Abdellatif Moudafi,et al.  Proximal methods for a class of bilevel monotone equilibrium problems , 2010, J. Glob. Optim..

[16]  Pham Ngoc Anh,et al.  Using the Banach Contraction Principle to Implement the Proximal Point Method for Multivalued Monotone Variational Inequalities , 2005 .

[17]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[18]  Antonino Maugeri,et al.  Equilibrium problems and variational models , 2003 .

[19]  L. Muu,et al.  The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions , 2011 .

[20]  Igor V. Konnov,et al.  Nonmonotone equilibrium problems: coercivity conditions and weak regularization , 2011, J. Glob. Optim..

[21]  Descent methods for mixed variational inequalities in a Hilbert space , 2001 .

[22]  P. Pardalos,et al.  Equilibrium problems : nonsmooth optimization and variational inequality models , 2004 .

[23]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[24]  Jen-Chih Yao,et al.  An Extragradient Method for Fixed Point Problems and Variational Inequality Problems , 2007 .

[25]  Vyacheslav V. Kalashnikov,et al.  Solving two-Level variational inequality , 1996, J. Glob. Optim..