Abstract:

In this paper, we study optimization problems with the sparsity constraints. Firstly we give the expressions of the Mordukhovich (the limiting) normal cone of sparsity constraint and its intersection with a polyhedral set, and then based on these expressions we present the first-order necessary conditions for sparsity constrained optimization.

Key words: Sparsity constrained optimization ·, Mordukhovich normal cone ·First-order necessary conditions