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.…
Author: | Christian Kanzow, Andreas B. Raharja, Alexandra Schwartz |
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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): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |