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Well-Posedness and Scalarization in Vector Optimization

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Abstract

In this paper, we study several existing notions of well- posedness for vector optimization problems. We separate 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.

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Authors and Affiliations

  1. Associate Professor, Dipartimento di Economia, Università dell’Insubria, Varese, Italy

    E. Miglierina

  2. Associate Professor, Dipartimento di Ricerche Aziendali, Università di Pavia, Pavia, Italy

    E. Molho

  3. Associate Professor, Dipartimento di Economia, Università dell’Insubria, Varese, Italy

    M. Rocca

Authors
  1. E. Miglierina
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  2. E. Molho
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  3. M. Rocca
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Additional information

The authors thank Professor C. Zălinescu for pointing out some inaccuracies in Ref. 11. His remarks allowed the authors to improve the present work.

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Miglierina, E., Molho, E. & Rocca, M. Well-Posedness and Scalarization in Vector Optimization. J Optim Theory Appl 126, 391–409 (2005). https://doi.org/10.1007/s10957-005-4723-1

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