Autori
Guerraggio, Angelo
Rocca, Matteo
Ginchev, Ivan

Titolo
On second-order conditions in vector optimization
Periodico
Università degli Studi dell'Insubria. Dipartimento di Economia. Quaderni di ricerca
Anno: 2002 - Fascicolo: 32 - Pagina iniziale: 1 - Pagina finale: 11

Starting from second-order conditions for C1,1 scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C1,1 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 Fr´echet 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.



Testo completo: http://eco.uninsubria.it/dipeco/quaderni/files/QF2002_32.pdf

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