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Calmness of efficient solution maps in parametric vector optimization

By Thai Doan Chuong, Alexander Kruger and J. C. Yao

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. © 2011 Springer Science+Business Media, LLC

Topics: Calmness, Coderivative, Efficient solution map, Implicit multifunction, Parametric vector optimization
Year: 2011
DOI identifier: 10.1007/s10898-011-9651-z
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