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Second-Order Conditions in C 1,1 Vector Optimization with Inequality and Equality Constraints

In: Recent Advances in Optimization

Author

Listed:
  • Ivan Ginchev

    (Technical University of Varna)

  • Angelo Guerraggio

    (University of Insubria)

  • Matteo Rocca

    (University of Insubria)

Abstract

Summary The present paper studies the following constrained vector optimization problem: minC f (x), g(x) ∈ −K, h(x) = 0, where f : ℝn → ℝm g : ℝn → ℝp are C 1,1 functions, h : ℝn → ℝq is C 2 function, and C ⊂ ℝm and K ⊂ ℝp are closed convex cones with nonempty interiors. Two type of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). In terms of the second-order Dini directional derivative second-order necessary conditions a point x 0 to be a w-minimizer and second-order sufficient conditions x 0 to be an i-minimizes of order two are formulated and proved. The effectiveness of the obtained conditions is shown on examples.

Suggested Citation

  • Ivan Ginchev & Angelo Guerraggio & Matteo Rocca, 2006. "Second-Order Conditions in C 1,1 Vector Optimization with Inequality and Equality Constraints," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 29-44, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_3
    DOI: 10.1007/3-540-28258-0_3
    as

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