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Increase-along-rays property for vector functions

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 extend to the vector case the notion of increasing along rays function. The proposed definition is given by means of a nonlinear scalarization through the so-called oriented distance function from a point to a set. We prove that the considered class of functions enjoys properties similar to those holding in the scalar case, with regard to optimization problems, relations with (generalized) convex functions and characterization in terms of Minty type variational inequalities. Key words: generalized convexity, increase-along-rays property, star-shaped set, Minty variational inequality.

Suggested Citation

  • 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.
    • Handle: RePEc:ins:quaeco:qf04015
    as

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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2004_24.pdf
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    References listed on IDEAS

    as
    1. Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "Variational inequalities in vector optimization," Economics and Quantitative Methods qf04020, Department of Economics, University of Insubria.
    2. X. M. Yang & X. Q. Yang & K. L. Teo, 2004. "Some Remarks on the Minty Vector Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 193-201, April.
    3. Miglierina Enrico & Molho Elena & Rocca Matteo, 2004. "Well-posedness and scalarization in vector optimization," Economics and Quantitative Methods qf0403, Department of Economics, University of Insubria.
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