Bucher, Max ; Schwartz, Alexandra (2018)
Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems.
In: Journal of Optimization Theory and Applications, 178 (2)
doi: 10.1007/s10957-018-1320-7
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation, we introduce second-order necessary and sufficient optimality conditions. Under such a second-order condition, we can guarantee local uniqueness of Mordukhovich stationary points. Finally, we use this observation to provide extended local convergence theory for a Scholtes-type regularization method, which guarantees the existence and convergence of iterates under suitable assumptions. This convergence theory can also be applied to other regularization schemes.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2018 |
| Autor(en): | Bucher, Max ; Schwartz, Alexandra |
| Art des Eintrags: | Bibliographie |
| Titel: | Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems |
| Sprache: | Englisch |
| Publikationsjahr: | August 2018 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Optimization Theory and Applications |
| Jahrgang/Volume einer Zeitschrift: | 178 |
| (Heft-)Nummer: | 2 |
| DOI: | 10.1007/s10957-018-1320-7 |
| URL / URN: | https://doi.org/10.1007/s10957-018-1320-7 |
| Kurzbeschreibung (Abstract): | We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation, we introduce second-order necessary and sufficient optimality conditions. Under such a second-order condition, we can guarantee local uniqueness of Mordukhovich stationary points. Finally, we use this observation to provide extended local convergence theory for a Scholtes-type regularization method, which guarantees the existence and convergence of iterates under suitable assumptions. This convergence theory can also be applied to other regularization schemes. |
| Freie Schlagworte: | Mathematics - Optimization and Control (math.OC) |
| Fachbereich(e)/-gebiet(e): | Exzellenzinitiative Exzellenzinitiative > Graduiertenschulen Exzellenzinitiative > Graduiertenschulen > Graduate School of Computational Engineering (CE) 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Optimierung |
| Hinterlegungsdatum: | 11 Sep 2017 12:51 |
| Letzte Änderung: | 23 Aug 2018 08:02 |
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