On necessity of L-stationarity in Nonlinear Optimization with a Sparsity Constraint

Abstract

In this paper, we investigate a necessary optimality condition for a specific problem in nonlinear programming, called sparsity constrained problem. This model involves minimizing a continuously differentiable function over a sparsity constraint. We show that L-stationarity is necessary for optimality in sparsity constrained problems in general. This important property has been proved in the literature under Lipschitzness of the gradient mapping../files/site1/files/61/6(1).pdf

Keywords

• nonlinear programming
• sparsity constrained problems
• l-stationarity
• optimality condition