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Mathematical Programs with Cardinality Constraints: Reformulation by Complementarity-Type Conditions and a Regularization Method
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-1836-4200
University of Würzburg, Germany. (Institute of Mathematics)
Technical University of Darmstadt, Germany. (Graduate School of Computational Engineering)
2016 (English)In: SIAM Journal on Optimization, ISSN 1052-6234, E-ISSN 1095-7189, Vol. 26, no 1, p. 397-425Article in journal (Refereed) Published
Abstract [en]

Optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; the relation between the local minima is also discussed in detail. Since our reformulation is a minimization problem in continuous variables, it allows to apply ideas from that field to cardinality-constrained problems. Here, in particular, we therefore also derive suitable stationarity conditions and suggest an appropriate regularization method for the solution of optimization problems with cardinality constraints. This regularization method is shown to be globally convergent to a Mordukhovich-stationary point. Extensive numerical results are given to illustrate the behavior of this method.

Place, publisher, year, edition, pages
2016. Vol. 26, no 1, p. 397-425
Keyword [en]
Cardinality constraints, global minima, local minima, stationary points, M-stationarity, relaxation, regularization method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-124611DOI: 10.1137/140978077ISI: 000373631500015OAI: oai:DiVA.org:liu-124611DiVA, id: diva2:901202
Available from: 2016-02-06 Created: 2016-02-06 Last updated: 2018-01-26Bibliographically approved

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Burdakov, Oleg

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