An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

Abstract A reformulation of cardinality-constrained optimization problems into continuous nonlinear with an orthogonality-type constraint has gained some popularity during the last few years. Due to special structure constraints, violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast this, we investigate viability a safeguarded multiplier penalty method without any problem-tailored modifications solve reformulated problem. We prove global convergence towards (essentially strongly) stationary point under suitable quasinormality qualification. Numerical experiments illustrating performance in comparison regularization-based approaches are provided.