Equivalence of Equilibrium Problems and Least Element Problems

Y.-P. Fang () and N.-J. Huang ()
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Y.-P. Fang: Sichuan University, Chengdu
N.-J. Huang: Sichuan University, Chengdu

Journal of Optimization Theory and Applications, 2007, vol. 132, issue 3, No 4, 422 pages

Abstract: 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.

Keywords: Strictly monotone functions; Z-function; Equilibrium problems; Feasible sets; Least element problems (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9186-0

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