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On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints

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Abstract

In this note, we prove that the convergence results for vector optimization problems with equilibrium constraints presented in Wu and Cheng (J. Optim. Theory Appl. 125, 453–472, 2005) are not correct. Actually, we show that results of this type cannot be established at all. This is due to the possible lack, even under nice assumptions, of lower convergence of the solution map for equilibrium problems, already deeply investigated in Loridan and Morgan (Optimization 20, 819–836, 1989) and Lignola and Morgan (J. Optim. Theory Appl. 93, 575–596, 1997).

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni R. Caccioppoli, Facoltá di Ingegneria, Università di Napoli, Via Claudio 21, 80125, Napoli, Italy

    M. B. Lignola

  2. Dipartimento di Matematica e Statistica, Università di Napoli, Complesso Universitario Monte S. Angelo, Via Cintia, 80126, Napoli, Italy

    J. Morgan

Authors
  1. M. B. Lignola
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  2. J. Morgan
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Correspondence to J. Morgan.

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Communicated by H.P. Benson.

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Lignola, M.B., Morgan, J. On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints. J Optim Theory Appl 133, 117–121 (2007). https://doi.org/10.1007/s10957-007-9198-9

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  • DOI: https://doi.org/10.1007/s10957-007-9198-9

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