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343. Partially non-convex minimax theorem and applications to remoteness of sets and functions
Invited abstract in session TC-42: Variational Analysis and Subdifferential techniques, stream Variational Analysis and Continuous Optimization.
Tuesday, 12:30-14:00Room: 98 (building: 306)
Authors (first author is the speaker)
| 1. | Mohammed Ibrahim Abdelkayoum Ghitri
|
| Mathematics, Universidad de Alicante | |
| 2. | Abderrahim Hantoute
|
| Mathematics, Universidad de Alicante |
Abstract
We propose two new variants of the well-known Fan’s minimax theorem, weakening the assumptions of convexity and lower semi-continuity used in the convex-concave standard version. Namely, the convexity and lower semi-continuity are only required on a smaller set which does not have to be convex or compact. In this case, the bi-function may take extended values on the given pair of convex sets. A second variant is then given when the bi-function is finite on these sets, removing the lower semi-continuity condition.These results are next used to study the remoteness of sets and functions in Hilbert spaces.
Key words: Minimax theorem, convexity, remotal sets and functions.
Keywords
- Convex Optimization
- Continuous Optimization
Status: accepted
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