Levitin-Polyak well-posedness for equilibrium problems with the lexicographic order. (English) Zbl 1481.90296
Summary: The aim of this work is to investigate optimization-related problems with the objective spaces ordered by the lexicographic cones, including parametric lexicographic equilibrium problems and optimization problems with lexicographic equilibrium constraints. We introduce concepts of Levitin-Polyak well-posedness for these problems and establish a number of sufficient conditions for such properties. The assumptions are imposed directly on the data of the problems and really verifiable. We do not need to suppose the existence (and/or convexity, compactness) of the solution set because it is proved using the mentioned assumptions on the data. Moreover, our assumptions are more relaxed than those which are usually imposed.
Keywords:
lexicographic equilibrium problem; optimization problem with lexicographic equilibrium constraints; Levitin-Polyak well-posedness; potential game; nontransitive consumerReferences:
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