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Well-posedness in vector optimization and scalarization results

Author

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  • Rocca Matteo

    (Department of Economics, University of Insubria, Italy)

  • Papalia Melania

    (Department of Economics, University of Insubria, Italy)

Abstract

In this paper, we give a survey on well-posedness notions of Tykhonov's type for vector optimization problems and the links between them with respect to the classification proposed by Miglierina, Molho and Rocca. We consider also the notions of extended well-posedness introduced by X.X. Huang in the nonparametric case to complete the hierchical structure characterizing these concepts. Finally we propose a review of some theoretical results in vector optimization mainly related to different notions of scalarizing functions, linear and nonlinear, introduced in the last decades, to simplify the study of various well-posedness properties.

Suggested Citation

  • Rocca Matteo & Papalia Melania, 2008. "Well-posedness in vector optimization and scalarization results," Economics and Quantitative Methods qf0807, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0807
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2008_7.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. G. P. Crespi & A. Guerraggio & M. Rocca, 2007. "Well Posedness in Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 213-226, January.
    3. M. Durea, 2007. "Scalarization for pointwise well-posed vectorial problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 409-418, December.
    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. 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.
    6. 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.
    7. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
    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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