A modified projection method for solving co-coercive variational inequalities

Abstract This paper presents a modified projection method for solving variational inequalities, which can be viewed as an improvement of the method of Yan, Han and Sun [X.H. Yan, D.R. Han, W.Y. Sun, A modified projection method with a new direction for solving variational inequalities, Applied Mathematics and Computation 211 (2009) 118–129], by adopting a new prediction step. Under the same assumptions, we establish the global convergence of the proposed algorithm. Some preliminary computational results are reported.

[1]  B. Curtis Eaves,et al.  On the basic theorem of complementarity , 1971, Math. Program..

[2]  P. Tseng On linear convergence of iterative methods for the variational inequality problem , 1995 .

[3]  P. Tseng,et al.  Modified Projection-Type Methods for Monotone Variational Inequalities , 1996 .

[4]  A. Goldstein Convex programming in Hilbert space , 1964 .

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

[6]  Deren Han,et al.  Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities , 2004, Eur. J. Oper. Res..

[7]  Wenyu Sun,et al.  A modified projection method with a new direction for solving variational inequalities , 2009, Appl. Math. Comput..

[8]  L. Liao,et al.  Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities , 2002 .

[9]  Min Li,et al.  A modified descent method for co-coercive variational inequalities , 2008, Eur. J. Oper. Res..

[10]  Naihua Xiu,et al.  Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities , 2001 .

[11]  E. Polak,et al.  Constrained Minimization Problems in Finite-Dimensional Spaces , 1966 .

[12]  Bingsheng He,et al.  Self-adaptive projection method for co-coercive variational inequalities , 2009, Eur. J. Oper. Res..

[13]  G. M. Korpelevich The extragradient method for finding saddle points and other problems , 1976 .

[14]  Masao Fukushima,et al.  A globally convergent Newton method for solving strongly monotone variational inequalities , 1993, Math. Program..

[15]  T. Zhu,et al.  A simple proof for some important properties of the projection mapping , 2004 .

[16]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[17]  E. Khobotov Modification of the extra-gradient method for solving variational inequalities and certain optimization problems , 1989 .

[18]  Boris Polyak,et al.  Constrained minimization methods , 1966 .

[19]  Wenyu Sun,et al.  A self-adaptive projection method with improved step-size for solving variational inequalities , 2008, Comput. Math. Appl..

[20]  Muhammad Aslam Noor,et al.  Some new projection methods for variational inequalities , 2003, Appl. Math. Comput..