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Well Posedness in Vector Optimization Problems and Vector Variational Inequalities

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Abstract

In this paper, we give notions of well posedness for a vector optimization problem and a vector variational inequality of the differential type. First, the basic properties of well-posed vector optimization problems are studied and the case of C-quasiconvex problems is explored. Further, we investigate the links between the well posedness of a vector optimization problem and of a vector variational inequality. We show that, under the convexity of the objective function f, the two notions coincide. These results extend properties which are well known in scalar optimization.

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Authors and Affiliations

  1. Université de la Vallée d’Aoste, Facoltà di Economia, Aosta, Italia

    G. P. Crespi (Assistant Professor)

  2. Dipartimento di Economia, Università dell’Insubria, Varese, Italia

    A. Guerraggio (Professor) & M. Rocca (Professor)

Authors
  1. G. P. Crespi
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  2. A. Guerraggio
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  3. M. Rocca
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Correspondence to G. P. Crespi.

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Communicated by F. Giannessi

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Crespi, G.P., Guerraggio, A. & Rocca, M. Well Posedness in Vector Optimization Problems and Vector Variational Inequalities. J Optim Theory Appl 132, 213–226 (2007). https://doi.org/10.1007/s10957-006-9144-2

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  • DOI: https://doi.org/10.1007/s10957-006-9144-2

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