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Variational inequalities in vector optimization

Listed author(s):
  • 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)

Registered author(s):

    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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    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
    Handle: RePEc:ins:quaeco:qf04020
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