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Dini Set-Valued Directional Derivative in Locally Lipschitz Vector Optimization

Author

Listed:
  • I. Ginchev

    (University of Insubria)

  • A. Guerraggio

    (University of Insubria)

  • M. Rocca

    (University of Insubria)

Abstract

The present paper studies the following constrained vector optimization problem: min C f(x), g(x)∈−K, h(x)=0, where f:ℝ n →ℝ m , g:ℝ n →ℝ p and h:ℝ n →ℝ q are locally Lipschitz functions and C⊂ℝ m , K⊂ℝ p are closed convex cones. In terms of the Dini set-valued directional derivative, first-order necessary and first-order sufficient conditions are obtained for a point x 0 to be a w-minimizer (weakly efficient point) or an i-minimizer (isolated minimizer of order 1). It is shown that, under natural assumptions (given by a nonsmooth variant of the implicit function theorem for the equality constraints), the obtained conditions improve some given by Clarke and Craven. Further comparison is done with some recent results of Khanh, Tuan and of Jiiménez, Novo.

Suggested Citation

  • I. Ginchev & A. Guerraggio & M. Rocca, 2009. "Dini Set-Valued Directional Derivative in Locally Lipschitz Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 87-105, October.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:1:d:10.1007_s10957-009-9551-2
    DOI: 10.1007/s10957-009-9551-2
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    References listed on IDEAS

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    1. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
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    Cited by:

    1. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    2. Thai Doan Chuong, 2019. "Optimality and Duality in Nonsmooth Conic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 471-489, November.

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