Duality for Sets of Strong Slater Points
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| Title: | Duality for Sets of Strong Slater Points |
|---|---|
| Authors: | Rodríguez Álvarez, Margarita | Vicente-Pérez, José |
| Research Group/s: | Laboratorio de Optimización (LOPT) |
| Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
| Keywords: | Strong Slater condition | Linear inequality system | Existence theorems | Duality |
| Issue Date: | 7-Mar-2023 |
| Publisher: | Springer Nature |
| Citation: | Set-Valued and Variational Analysis. 2023, 31:10. https://doi.org/10.1007/s11228-023-00670-7 |
| Abstract: | The strong Slater condition plays a significant role in the stability analysis of linear semi-infinite inequality systems. This piece of work studies the set of strong Slater points, whose non-emptiness guarantees the fullfilment of the strong Slater condition. Given a linear inequality system, we firstly establish some basic properties of the set of strong Slater points. Then, we derive dual characterizations for this set in terms of the data of the system, following similar characterizations provided also for the set of Slater points and the solution set of the given system, which are based on the polarity operators for evenly convex and closed convex sets. Finally, we present two geometric interpretations and apply our results to analyze the strict inequality systems defined by lower semicontinuous convex functions. |
| Sponsor: | This research was partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22, and by the Generalitat Valenciana, Grant AICO/2021/165. |
| URI: | http://hdl.handle.net/10045/132669 |
| ISSN: | 1877-0533 (Print) | 1877-0541 (Online) |
| DOI: | 10.1007/s11228-023-00670-7 |
| Language: | eng |
| Type: | info:eu-repo/semantics/article |
| Rights: | © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Peer Review: | si |
| Publisher version: | https://doi.org/10.1007/s11228-023-00670-7 |
| Appears in Collections: | INV - LOPT - Artículos de Revistas |
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| File | Description | Size | Format | |
|---|---|---|---|---|
 Rodriguez_Vicente-Perez_2023_Set-ValuedVarAnal.pdf | 535,93 kB | Adobe PDF | Open Preview | |
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