Sequential optimality conditions for cardinality-constrained optimization problems with applications
This paper considers the cardinality-constrained problem, a special type of very hard optimization problems where even testing for feasibility is NP-complete. Traditional algorithms work by converting the problem to a mixed integer programming problem and more recent approaches use sparse optimization methods. The authors begin by presenting the preliminaries and background definitions of this very interesting problem, followed by the main contribution of the article in the form of a sequential optimality condition and a cone-continuity-type constraint qualification, for use with sparse optimization. The article then demonstrates the application of the method to regularization methods and augmented Lagrange methods, although the full result on the application to global regularization remains an open problem.
cone-continuity type constraint qualification
scientific article; zbMATH DE number 7379937
scientific article