An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

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

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 3, No 5, 793-813

Abstract: Abstract 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 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.

Keywords: Cardinality constraints; Augmented Lagrangian; Global convergence; Stationarity; Quasinormality constraint qualification (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01854-7

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