94. Closed convex sets that are both Motzkin decomposable and generalized Minkowski sets
Invited abstract in session FD-3: Variational techniques in optimization, stream Variational analysis: theory and algorithms.
Friday, 14:10 - 15:50Room: M:J
Authors (first author is the speaker)
| 1. | Juan Enrique MartÃnez-Legaz
|
| Departament d'Economia, Universitat Autònoma de Barcelona | |
| 2. | Cornel Pintea
|
| Babes Bolyai University |
Abstract
We consider and characterize closed convex subsets of the Euclidean space that are simultaneously Motzkin decomposable and generalized Minkowski sets or, shortly, MdgM sets. We also prove the existence of suitably defined fixed points for (possibly multivalued) functions defined on MdgM sets along with existence of classical fixed points for some single valued self functions of MdgM sets. The first mentioned type of existence results are based on the Kakutani fixed point theorem, and the second type are obtained by combining the Brouwer fixed point theorem with the Banach contraction principle.
Keywords
- Convex and non-smooth optimization
Status: accepted
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