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Higher-order optimality conditions for strict local minima

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  • Bienvenido Jiménez
  • Vicente Novo

Abstract

In this work, we study a nonsmooth optimization problem with generalized inequality constraints and an arbitrary set constraint. We present necessary conditions for a point to be a strict local minimizer of order k in terms of higher-order (upper and lower) Studniarski derivatives and the contingent cone to the constraint set. In the same line, when the initial space is finite dimensional, we develop sufficient optimality conditions. We also provide sufficient conditions for minimizers of order k using the lower Studniarski derivative of the Lagrangian function. Particular interest is put for minimizers of order two, using now a special second order derivative which leads to the Fréchet derivative in the differentiable case. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Bienvenido Jiménez & Vicente Novo, 2008. "Higher-order optimality conditions for strict local minima," Annals of Operations Research, Springer, vol. 157(1), pages 183-192, January.
    • Handle: RePEc:spr:annopr:v:157:y:2008:i:1:p:183-192:10.1007/s10479-007-0197-x
    DOI: 10.1007/s10479-007-0197-x
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    1. Bienvenido Jiménez & Vicente Novo, 2003. "Second order necessary conditions in set constrained differentiable vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 299-317, November.
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    Cited by:

    1. Nguyen Hoang Anh & Phan Khanh, 2014. "Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives," Journal of Global Optimization, Springer, vol. 58(4), pages 693-709, April.

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