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Recent Advances in Optimization pp 29–44Cite as

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

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 563))

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.

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Author information

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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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Avignon, 33, rue Louis Pasteur, 84000, Avignon, France

    Alberto Seeger

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© 2006 Springer-Verlag Berlin Heidelberg

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Ginchev, I., Guerraggio, A., Rocca, M. (2006). Second-Order Conditions in C 1,1 Vector Optimization with Inequality and Equality Constraints. In: Seeger, A. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28258-0_3

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