An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems
Zitieren Sie bitte immer diese URN: urn:nbn:de:bvb:20-opus-269166
- A reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulatedA reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.…
Autor(en): | Christian Kanzow, Andreas B. Raharja, Alexandra Schwartz |
---|---|
URN: | urn:nbn:de:bvb:20-opus-269166 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Journal of Optimization Theory and Applications |
ISSN: | 1573-2878 |
Erscheinungsjahr: | 2021 |
Band / Jahrgang: | 189 |
Heft / Ausgabe: | 3 |
Seitenangabe: | 793–813 |
Originalveröffentlichung / Quelle: | Journal of Optimization Theory and Applications 2021, 189(3):793–813. DOI: 10.1007/s10957-021-01854-7 |
DOI: | https://doi.org/10.1007/s10957-021-01854-7 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Freie Schlagwort(e): | augmented Lagrangian; cardinality constraints; global convergence; quasinormality constraint qualification; stationarity |
Datum der Freischaltung: | 13.06.2022 |
Lizenz (Deutsch): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |