|
|
|
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.
|
|
|
|
Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
|
|
