Sequential optimality conditions for cardinality-constrained optimization problems with applications

Christian Kanzow (), Andreas B. Raharja () and Alexandra Schwartz ()
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Christian Kanzow: University of Würzburg
Andreas B. Raharja: University of Würzburg
Alexandra Schwartz: Technische Universität Dresden

Computational Optimization and Applications, 2021, vol. 80, issue 1, No 7, 185-211

Abstract: Abstract 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 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.

Keywords: Cardinality constraints; Sequential optimality condition; Cone-continuity type constraint qualification; Relaxation method; Augmented Lagrangian method (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-021-00298-z

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