Autori
Crespi, Giovanni Paolo
Rocca, Matteo
Ginchev, Ivan

Titolo
Variational inequalities in vector optimization
Periodico
Università degli Studi dell'Insubria. Dipartimento di Economia. Quaderni di ricerca
Anno: 2004 - Fascicolo: 31 - Pagina iniziale: 1 - Pagina finale: 16

In this paper we investigate the links among generalized scalar variational inequalities of differential type, vector variational inequalities and vector optimization problems. The considered scalar variational inequalities are obtained through a nonlinear scalarization by means of the so called ”oriented distance” function. In the case of Stampacchia-type variational inequalities, the solutions of the proposed ones coincide with the solutions of the vector variational inequalities introduced by Giannessi. For Minty-type variational inequalities, analogous coincidence happens under convexity hypotheses. Furthermore, the considered variational inequalities reveal useful in filling a gap between scalar and vector variational inequalities. Namely, in the scalar case Minty variational inequalities of differential type represent a sufficient optimality condition without additional assumptions, while in the vector case the convexity hypothesis was needed. Moreover it is shown that vector functions admitting a solution of the proposed Minty variational inequality enjoy some well posedness properties, analogously to the scalar case.



Testo completo: http://eco.uninsubria.it/dipeco/quaderni/files/QF2004_31.pdf

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