An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

Please always quote using this 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.show moreshow less

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Metadaten
Author: Christian Kanzow, Andreas B. Raharja, Alexandra Schwartz
URN:urn:nbn:de:bvb:20-opus-269166
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Language:English
Parent Title (English):Journal of Optimization Theory and Applications
ISSN:1573-2878
Year of Completion:2021
Volume:189
Issue:3
Pagenumber:793–813
Source: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
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:augmented Lagrangian; cardinality constraints; global convergence; quasinormality constraint qualification; stationarity
Release Date:2022/06/13
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International