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|Paper IPM / M / 16299||
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.
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