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

M. B. Lignola and Jacqueline Morgan
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M. B. Lignola: Università di Napoli

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 1, No 9, 117-121

Abstract: 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).

Keywords: Vector optimization; Equilibrium constraints; Bilevel programming problems; ε-Solutions; Convergences for set-valued mappings (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9198-9

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