- | ||||
|
![]()
|
BILEVEL OPTIMIZATION AS A REGULARIZATION APPROACH TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS
Bui Van Dinh(vandinhb 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2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity ) Category 3: Global Optimization Citation: UNPUBLISHED: 1)report number: 1; 2)Institution address: 1.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 Download: [PDF] Entry Submitted: 01/20/2013 Modify/Update this entry | ||
Visitors | Authors | More about us | Links | |
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository
|
Submit Update Policies |
Coordinator's Board Classification Scheme Credits Give us feedback |
Optimization Journals, Sites, Societies | |
![]() |