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A note on the combination of equilibrium problems

Author

Listed:
  • Nguyen Thi Thanh Ha

    (Le Quy Don Technical University)

  • Tran Thi Huyen Thanh

    (Le Quy Don Technical University)

  • Nguyen Ngoc Hai

    (Trade Union University)

  • Hy Duc Manh

    (Le Quy Don Technical University)

  • Bui Dinh

    (Le Quy Don Technical University)

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.

Suggested Citation

  • Nguyen Thi Thanh Ha & Tran Thi Huyen Thanh & Nguyen Ngoc Hai & Hy Duc Manh & Bui Dinh, 2020. "A note on the combination of equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 311-323, April.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:2:d:10.1007_s00186-019-00690-w
    DOI: 10.1007/s00186-019-00690-w
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