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Well-posedness and scalarization in vector optimization

Author

Listed:
  • Miglierina Enrico

    (Department of Economics, University of Insubria, Italy)

  • Molho Elena

    (University of Pavia, Italy)

  • Rocca Matteo

    (Department of Economics, University of Insubria, Italy)

Abstract

In this paper we study several existing notions of well-posedness for vector optimization problems. We distinguish them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well-posed.

Suggested Citation

  • 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.
    • Handle: RePEc:ins:quaeco:qf0403
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2004_7.pdf
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    References listed on IDEAS

    as
    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. X. X. Huang, 2000. "Extended Well-Posedness Properties of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 165-182, July.
    3. Loridan, P. & Morgan, J. & Raucci, R., 1997. "Convergence of Minimal and Approximate Minimal Elements of Sets in Partially Ordered Vector Spaces," Papiers d'Economie Mathématique et Applications 97.94, Université Panthéon-Sorbonne (Paris 1).
    4. X. X. Huang, 2001. "Extended and strongly extended well-posedness of set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 101-116, April.
    5. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    6. 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.
    7. E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
    8. X. X. Huang, 2001. "Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 671-684, March.
    9. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
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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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