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Paper   IPM / M / 16299
School of Mathematics
  Title:   Nonsmooh sparsity constrained optimization problems: Optimality conditions
  Author(s):  Soghra Nobakhtian (Joint with N. Movahedia and M. Saarabadan)
  Status:   Published
  Journal: Optim. Lett
  Vol.:  13
  Year:  2019
  Pages:   1027-1038
  Supported by:  IPM
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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