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On second-order conditions in vector optimization

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Author Info
Ginchev Ivan () (Department of Mathematics, Technical University of Varna, Bulgaria)
Guerraggio Angelo () (Department of Economics, University of Insubria, Italy)
Rocca Matteo () (Department of Economics, University of Insubria, Italy)
Abstract

Starting from second-order conditions for C 1,1 scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C 1,1 vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof of the COnjecture in the case of C1,1 function (called the nonsmooth case) will be given in another paper. The present paper provides the background leading to its correct formulation. Using Lagrange multipliers technique, we prove the COnjecture in the case of twice Fréchet differentiable function (called the smooth case) and show on example the effectiveness of the obtained conditions. Another example shows, that in the nonsmooth case it is important to take into account the whole set of Lagrange multipliers, instead of dealing with a particular multiplier.

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Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0218.

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Length: 13 pages
Date of creation: Oct 2002
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Handle: RePEc:ins:quaeco:qf0218

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Keywords: nonsmooth vector optimization; second-order conditions;

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  1. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "From scalar to vector optimization," Economics and Quantitative Methods qf0305, Department of Economics, University of Insubria. [Downloadable!]
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