Second-order conditions in C
1,1 constrained vector optimization |
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Authors: | Ivan Ginchev Angelo Guerraggio Matteo Rocca |
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Institution: | (1) Department of Mathematics, Technical University of Varna, Studentska Str. 1, 9010 Varna, Bulgaria;(2) Department of Economics, University of Insubria, Via Ravasi 2, 21100 Varese, Italy |
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Abstract: | We consider the constrained vector optimization problem min C f(x), g(x) ∈ ?K, where f:? n →? m and g:? n →? p are C 1,1 functions, and C ![></img> </span>?<sup> <em>p</em> </sup> are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely <em>w</em>-minimizers (weakly efficient points) and <em>i</em>-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point <em>x</em> <sup>0</sup> to be a <em>w</em>-minimizer and second-order sufficient conditions for <em>x</em> <sup>0</sup> to be an <em>i</em>-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmäki, K?í?ek 21].</td>
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Keywords: | 90C29 90C30 90C46 49J52 |
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