Invariant-point theorems and existence of solutions to optimization-related problems

Phan Khanh () and Vo Long ()

Journal of Global Optimization, 2014, vol. 58, issue 3, 545-564

Abstract: To consider existence of solutions to various optimization-related problems, we first develop some equivalent versions of invariant-point theorems. Next, they are employed to derive sufficient conditions for the solution existence for two general models of variational relation and inclusion problems. We also prove the equivalence of these conditions with the above-mentioned invariant-point theorems. In applications, we include consequences of these results to a wide range of particular cases, from relatively general inclusion problems to classical results as Ekeland’s variational principle, and practical situations like traffic networks and non-cooperative games, to illustrate application possibilities of our general results. Many examples are provided to explain advantages of the obtained results and also to motivate in detail our problem settings. Copyright Springer Science+Business Media New York 2014

Keywords: Invariant points; Existence of solutions; Variational relation and inclusion problems; Nash equilibria; Traffic networks; Equilibrium problems; Constrained minimization; 90C26; 90C48; 47J22; 49J40 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-013-0065-y

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