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- Title
FROM DETERMINISTIC TO STOCHASTIC EQUILIBRIUM PROBLEMS: EXISTENCE OF SOLUTIONS AND APPLICATION TO CONVEX PROGRAMMING.
- Authors
MANSOUR, M. AIT; ELAKRI, R-.A.; LAGHDIR, M.
- Abstract
In this paper, by means of Castaing representation Theorem, we extend the results by M. Ait Mansour, R-.A. Elakri and M. Laghdir [Equilibrium and quasi-equilibrium problems under j-quasimonotonicity and j-quasiconvexity, Existence, stability and applications, Minimax Theory and its Applications, 2 (2) (2017), 175-229] to random equilibrium problems wherein the objective data are subject to a random perturbation. We obtain deterministic as well as random (or measurable) and integral solutions to random equilibrium problems. The case when the random parameter has a probability of realization suggests us to introduce stochastic formulations of equilibria covering the expected value approach and the almost sure method. Thus, we prove the existence of two further kinds of equilibria under uncertainty: almost sure solutions and expected stochastic equilibrium points. Finally, we present an application to stochastic convex and quasiconvex programming for which we establish the existence of almost sure minimizers.
- Subjects
EQUILIBRIUM; CONVEX programming; VARIATIONAL inequalities (Mathematics); FIXED point theory; STOCHASTIC analysis
- Publication
Le Matematiche, 2018, Vol 73, Issue 2, p213
- ISSN
0373-3505
- Publication type
Article
- DOI
10.4418/2018.73.2.1