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Equivalence of Equilibrium Problems and Least Element Problems

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Abstract

In this paper, we introduce the concept of feasible set for an equilibrium problem with a convex cone and generalize the notion of a Z-function for bifunctions. Under suitable assumptions, we derive some equivalence results of equilibrium problems, least element problems, and nonlinear programming problems. The results presented extend some results of [Riddell, R.C.: Equivalence of nonlinear complementarity problems and least element problems in Banach lattices. Math. Oper. Res. 6, 462–474 (1981)] to equilibrium problems.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    Y.-P. Fang & N.-J. Huang

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  1. Y.-P. Fang
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  2. N.-J. Huang
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Correspondence to Y.-P. Fang.

Additional information

Communicated by S. Schaible

This work was supported by the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005) and the Educational Science Foundation of Chongqing (KJ051307).

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Fang, YP., Huang, NJ. Equivalence of Equilibrium Problems and Least Element Problems. J Optim Theory Appl 132, 411–422 (2007). https://doi.org/10.1007/s10957-007-9186-0

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  • DOI: https://doi.org/10.1007/s10957-007-9186-0

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