Relaxed method for optimization problems with cardinality constraints

Yan-Chao Liang () and Gui-Hua Lin ()
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Yan-Chao Liang: Henan Normal University
Gui-Hua Lin: Shanghai University

Journal of Global Optimization, 2024, vol. 88, issue 2, No 3, 359-375

Abstract: Abstract In this paper, we review optimality conditions and constraint qualifications for the optimization problems with cardinality constraints (OPCC). OPCC is a class of optimization problems with important applications. In this paper, we provide a relaxed method for OPCC. We show that the Mangasarian-Fromovitz constraint qualification or constant positive linear dependence constraint qualification holds for the relaxed problem under some mild conditions. We provide that the local solution of the relaxed problem converges to the M-stationarity of OPCC under appropriate conditions. Furthermore, we obtain that the inexact stationary points of relaxed problem converges to the M-stationarity of OPCC under very weaker conditions. Numerical experiments show the effectiveness of the proposed method.

Keywords: Optimization problems with cardinality constraint; Relaxed method; M-stationarity; S-stationarity; Global convergence; Constraint qualifications.; 90C30; 90C33; 90C46 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01317-5

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