New criteria for existence of solutions for equilibrium problems
| Autor: | Balaj, M., Castellani, M., Giuli, M. |
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| Rok vydání: | 2023 |
| Předmět: |
Generalized convexity
Generalized monotonicity Business Management and Accounting (miscellaneous) Management Science and Operations Research Statistics Probability and Uncertainty Equilibrium problem Quasiequilibrium problem Generalized convexity Generalized monotonicity Equilibrium problem Quasiequilibrium problem Management Information Systems |
| Zdroj: | Computational Management Science. 20 |
| ISSN: | 1619-6988 1619-697X |
| Popis: | Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed point and saddle point problems, and noncooperative games as particular cases. In this paper sufficient conditions for the existence of solutions of an equilibrium problem are given by weakening the assumption of quasiconvexity of the involved equilibrium bifunction. The existence of solutions is established both in presence of compactness of the feasible set as well with a coercivity assumption. The results are obtained in an infinite dimensional setting, and they are based on the so called finite solvability property which is weaker than the recently introduced finite intersection property and in turn, weaker than most common cyclic and proper quasimonotonicity. Some examples are presented to illustrate the various cases in which other existence results for equilibrium problems do not apply. Finally, applications to the solution of quasiequilibrium problems, quasioptimization problems and generalized quasivariational inequalities are discussed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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