Calmness of efficient solution maps in parametric vector optimization

Calmness of efficient solution maps in parametric vector optimization

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Article ID: iaor201110506
Volume: 51
Issue: 4
Start Page Number: 677
End Page Number: 688
Publication Date: Dec 2011
Journal: Journal of Global Optimization
Authors: , ,
Keywords: heuristics, programming: multiple criteria
Abstract:

The paper is concerned with the stability theory of the efficient solution map of a parametric vector optimization problem. Utilizing the advanced tools of modern variational analysis and generalized differentiation, we study the calmness of the efficient solution map. More explicitly, new sufficient conditions in terms of the Fréchet and limiting coderivatives of parametric multifunctions for this efficient solution map to have the calmness at a given point in its graph are established by employing the approach of implicit multifunctions. Examples are also provided for analyzing and illustrating the results obtained.

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