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We study a cardinality-constrained optimisation problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly, we study some properties on the optimal solutions of this optimisation problem under some conditions. An equivalent reformulation of the problem under consideration is proposed. Based on the reformulation, we present a successive convex approximation method for the cardinality constrained optimisation problem. We prove that the method converges to a KKT point of the reformulation problem. Under some conditions, the KKT points of the reformulation problem are local optimisers of the original problem. Our numerical results on a limited diversified mean–variance portfolio selection problem demonstrate some promising results.

Cardinality-constrained programs with nonnegative variables and an SCA method