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

Ivan Ginchev (), Angelo Guerraggio () and Matteo Rocca ()
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Ivan Ginchev: Technical University of Varna
Angelo Guerraggio: University of Insubria
Matteo Rocca: University of Insubria

A chapter in Recent Advances in Optimization, 2006, pp 29-44 from Springer

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.

Keywords: Inequality Constraint; Vector Optimization; Implicit Function Theorem; Feasible Point; Nonempty Interior (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-28258-7_3

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DOI: 10.1007/3-540-28258-0_3

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