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Optimality conditions for nonsmooth semidefinite programming via convexificators

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Abstract

This study is devoted to the semidefinite optimization problems with inequality constraints. We use the notion of convexificators to establish optimality conditions for nonsmooth semidefinite optimization problems. Moreover, we introduce appropriate constraint qualifications to present the Karush–Kuhn–Tucker multipliers.

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Acknowledgments

The second author was partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Iran.

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Authors and Affiliations

  1. Department of Mathematics, University of Fasa, Fasa, Iran

    M. Golestani

  2. Department of Mathematics, University of Isfahan, Isfahan, Iran

    S. Nobakhtian

Authors
  1. M. Golestani
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  2. S. Nobakhtian
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Correspondence to S. Nobakhtian.

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Golestani, M., Nobakhtian, S. Optimality conditions for nonsmooth semidefinite programming via convexificators. Positivity 19, 221–236 (2015). https://doi.org/10.1007/s11117-014-0292-6

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