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Vietnam Journal of Mathematics 40:2&3(2012) 255-274

 

On Inexact Tikhonov and Proximal Point

Regularization Methods for Pseudomonotone

Equilibrium Problems

Pham Gia Hung1 and Le Dung Muu2

1Nha Trang University, 02 Nguyen Dinh Chieu, Nha Trang,

Khanh Hoa, Vietnam

2Institute of Mathematics, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received October 17, 2011

Revised April 4, 2012

Abstract. We investigate the inexact Tikhonov and proximal point regularization methods for pseudomonotone equilibrium problems. In this case, the regularized subproblems might not be strongly monotone, even not pseudomonotone. However, any iterative sequence of the regularized subproblems tends to the same solution, which, for the Tikhonov method, is the projection of the starting point onto the solution set of the original problem. This convergence result suggests algorithms for finding the limit point of the Tikhonov regularization method. Application to multivalued pseudomonotone variational inequalities is discussed.

2000 Mathematics Subject Classification. 49J40, 90C33, 47H17.

Keywords. Pseudomonotone equilibrium problem, inexact Tikhonov and proximal point methods, multivalued pseudomonotone variational inequality.

 

 

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