Ha, N.T.T. and Thanh, T.T.H. and Hai, N.N. and Manh, H.D. and Van Dinh, B. (2020) A note on the combination of equilibrium problems. Mathematical Methods of Operations Research, 91 (2). pp. 311-323. ISSN 14322994
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Abstract
We show that the solution set of a strictly convex combination of equilibrium problems is not necessarily contained in the corresponding intersection of solution sets of equilibrium problems even if the bifunctions defining the equilibrium problems are continuous and monotone. As a consequence, we show that some results given in some recent papers are not always true. Therefore different numerical methods for computing common solutions of families of equilibrium problems proposed in the literature may not converge under the monotonicity assumption. Finally, we prove that if the bifunctions are also parapseudomonotone, then the solution set of any strictly convex combination of a family of equilibrium problems is equivalent to the solution set of the intersection of the same family of equilibrium problems. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Item Type: | Article |
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Divisions: | Faculties > Faculty of Information Technology |
Identification Number: | 10.1007/s00186-019-00690-w |
Uncontrolled Keywords: | Operations research; Software engineering; Bifunctions; Equilibria; Equilibrium problem; Families of equilibria; Ky Fan inequality; Monotonicity; Solution set; Strictly convexes; Numerical methods |
Additional Information: | Language of original document: English. All Open Access, Green. |
URI: | http://eprints.lqdtu.edu.vn/id/eprint/9039 |