Sequential optimality conditions for cardinality-constrained optimization problems with applications

Please always quote using this URN: urn:nbn:de:bvb:20-opus-269052
  • Recently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improveRecently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improve existing results for a known regularization method by proving that it generates limit points satisfying the aforementioned optimality conditions even if the subproblems are only solved inexactly. And we show that, under a suitable Kurdyka–Łojasiewicz-type assumption, any limit point of a standard (safeguarded) multiplier penalty method applied directly to the reformulated problem also satisfies the optimality condition. These results are stronger than corresponding ones known for the related class of mathematical programs with complementarity constraints.show moreshow less

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Metadaten
Author: Christian Kanzow, Andreas B. Raharja, Alexandra Schwartz
URN:urn:nbn:de:bvb:20-opus-269052
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Language:English
Parent Title (English):Computational Optimization and Applications
ISSN:1573-2894
Year of Completion:2021
Volume:80
Issue:1
Pagenumber:185-211
Source:Computational Optimization and Applications 2021, 80(1):185-211. DOI: 10.1007/s10589-021-00298-z
DOI:https://doi.org/10.1007/s10589-021-00298-z
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:augmented Lagrangian method; cardinality constraints; conecontinuity type constraint qualification; relaxation method; sequential optimality condition
Release Date:2022/06/13
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International