BILEVEL OPTIMIZATION AS A REGULARIZATION APPROACH TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

Bui Van Dinh(vandinhbgmail.com)
Le Dung Muu(ldmuumath.ac.vn)
Pham Gia Hung(hwngpgyahoo.com.vn)

Abstract: We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Un- like monotone case, in pseudomonotone case, the regularized subprob- lems may not be strongly monotone, even not pseudomonotone. How- ever, every proximal trajectory weakly converges to the same limit, We use these properties to extend a viscosity-proximal point algorithm de- veloped in [29] to pseudomonotone equilibrium problems. Then we pro- pose a hybrid extragradient-cutting plane algorithm for approximating the limit point by solving a bilevel strongly convex optimization prob- lem. Finally, we show that by using this bilevel convex optimization, the proximal point method can be used for handling ill-possed pseu- domonotone equilibrium problems.

Keywords: Pseudomonotone equilibrium problem, inexact proximal point, bilevel optimization, hybrid extragradient-cutting algorithm, reg- ularization.

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 3: Global Optimization

Citation: UNPUBLISHED: 1)report number: 1; 2)Institution address: 1. Bui Van Dinh, Department of Mathematics, Le Quy Don University, No 100, Hoang Quoc Viet, Hanoi, Vietnam; 2. Pham Gia Hung, Nha Trang University, Nha Trang, Vietnam;3. Le Dung Muu, Institute of Mathematics, Hanoi, Vietnam; 3).Month/Year: 01/2013

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Entry Submitted: 01/20/2013
Entry Accepted: 01/20/2013
Entry Last Modified: 01/20/2013

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