Ekeland variational principles for set-valued functions with set perturbations. (English) Zbl 1442.58014
The paper under review is concerned with a set-valued version of the Ekeland variational principle. A feature of this main result is that the objective function is a set-valued map taking values in a real vector space \(K\) quasi-ordered by a convex cone and the perturbation consists
of a cone-convex subset \(H\) of \(K\) multiplied by the distance function. The main ingredients in the proof are the following: (i) a generalized nonconvex separation property; (ii) a pre-order principle. Various applications illustrate the main abstract result of this paper.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 58E30 | Variational principles in infinite-dimensional spaces |
| 49J53 | Set-valued and variational analysis |
| 65K10 | Numerical optimization and variational techniques |
| 90C26 | Nonconvex programming, global optimization |
| 90C48 | Programming in abstract spaces |
Keywords:
Ekeland variational principle; set-valued objective function; set perturbation; nonconvex separation functional; vector closure; \((C, \epsilon)\)-efficient solutionReferences:
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