Nonsmooth sparsity constrained optimization problems: optimality conditions

Abstract

This paper concerns a nonsmooth sparsity constrained optimization problem. We present first and second-order necessary and sufficient optimality conditions by using the concept of normal and tangent cones to the sparsity constraint set. Moreover, second-order tangent set to the sparsity constraint is described and then a new second-order necessary optimality condition is established. The results are illustrated by several examples. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.