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Second-order conditions in C1,1 constrained vector optimization

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Abstract

We consider the constrained vector optimization problem min C f(x), g(x) ∈ −K, where f:ℝn→ℝm and g:ℝn→ℝp are C1,1 functions, and Cℝm and Kℝp are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point x0 to be a w-minimizer and second-order sufficient conditions for x0 to be an i-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmäki, Křížek [21].

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Varna, Studentska Str. 1, 9010, Varna, Bulgaria

    Ivan Ginchev

  2. Department of Economics, University of Insubria, Via Ravasi 2, 21100, Varese, Italy

    Angelo Guerraggio & Matteo Rocca

Authors
  1. Ivan Ginchev
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  2. Angelo Guerraggio
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  3. Matteo Rocca
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Correspondence to Matteo Rocca.

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This paper is dedicated to R.T. Rockafellar whose works have guided and inspired us

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Ginchev, I., Guerraggio, A. & Rocca, M. Second-order conditions in C1,1 constrained vector optimization. Math. Program. 104, 389–405 (2005). https://doi.org/10.1007/s10107-005-0621-4

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  • DOI: https://doi.org/10.1007/s10107-005-0621-4

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