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Variational inequalities in vector optimization

Author

Listed:
  • Crespi Giovanni P.

    (Department of Economics, University of Insubria, Italy)

  • Ginchev Ivan

    (Department of Mathematics Varna, Bulgaria)

  • Rocca Matteo

    (Department of Economics, University of Insubria, Italy)

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].

Suggested Citation

  • Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "Variational inequalities in vector optimization," Economics and Quantitative Methods qf04020, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf04020
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2004_31.pdf
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    References listed on IDEAS

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    1. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
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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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