Ginchev Ivan () (Department of Mathematics Varna, Bulgaria) Guerraggio Angelo () (Department of Economics, University of Insubria, Italy) Rocca Matteo () (Department of Economics, University of Insubria, Italy)
Abstract
We consider the constrained vector optimization problem minC f(x), g(x) 2 -K, where f : Rn ! Rm and g : Rn Rp are C1,1 functions, and C Rm and K Rp are closed convex cones with nonempty interiors. Two type of solutions are important for our consideration, 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 a point x0 to be a w-minimizer and second-order sufficient conditions x0 to be a i-minimizer of order two. We discuss the possible reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanm¨aki, K?r´i?rek [20]. Key words: Vector optimization, C1,1 optimization, Dini derivatives, Second-order conditions, Duality.
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