TY  - JOUR
A1  - Kanzow, Christian
A1  - Raharja, Andreas B.
A1  - Schwartz, Alexandra
T1  - An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems
JF  - Journal of Optimization Theory and Applications
N2  - 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.
KW  - quasinormality constraint qualification
KW  - cardinality constraints
KW  - augmented Lagrangian
KW  - global convergence
KW  - stationarity
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-269166
SN  - 1573-2878
VL  - 189
IS  - 3
ER  -