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Bilevel optimization as a regularization approach to pseudomonotone equilibrium problems

Dinh, B.V. and Hung, P.G. and Muu, L.D. (2014) Bilevel optimization as a regularization approach to pseudomonotone equilibrium problems. Numerical Functional Analysis and Optimization, 35 (5). pp. 539-563. ISSN 1630563

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Abstract

We study properties of an inexact proximal point method for pseudomonotone equilibrium problems in real Hilbert spaces. Unlike monotone problems, in pseudomonotone problems, the regularized subproblems may not be strongly monotone, even not pseudomonotone. However, we show that every inexact proximal trajectory weakly converges to the same limit. We use these properties to extend a viscosity-proximal point algorithm developed in [28] to pseudomonotone equilibrium problems. Then we propose a hybrid extragradient-cutting plane algorithm for approximating the limit point by solving a bilevel strongly convex optimization problem. Finally, we show that by using this bilevel convex optimization, the proximal point method can be used for handling ill-possed pseudomonotone equilibrium problems. Copyright © Taylor & Francis Group, LLC.

Item Type: Article
Divisions: Faculties > Faculty of Information Technology
Identification Number: 10.1080/01630563.2013.813857
Uncontrolled Keywords: Algorithms; Convex optimization; Bi-level optimization; Convex optimization problems; Equilibrium problem; Proximal point method; Proximal Points; Regularization; Regularization approach; Strongly-monotones; Optimization
Additional Information: Language of original document: English.
URI: http://eprints.lqdtu.edu.vn/id/eprint/9985

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