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Variational inequalities in vector optimization

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  • Crespi Giovanni P.

    ()
    (Facoltà di Scienze Economiche Aosta, Italy)

  • Ginchev Ivan

    ()
    (Department of Mathematics Varna, Bulgaria)

  • Rocca Matteo

    ()
    (Department of Economics, University of Insubria, Italy)

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    Abstract

    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 [14, 15]. 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 [8]. 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 [4].

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    File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2004_31.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf04020.

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    Length: 18 pages
    Date of creation: Oct 2004
    Date of revision:
    Handle: RePEc:ins:quaeco:qf04020

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    Cited by:
    1. Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "Increase-along-rays property for vector functions," Economics and Quantitative Methods qf04015, Department of Economics, University of Insubria.

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