Calmness of efficient solution maps in parametric vector optimization

Authors:
T. D. Chuong;A. Y. Kruger;J. -C. Yao
Affiliations:
Department of Mathematics, Dong Thap University, Cao Lanh City, Vietnam;Centre for Informatics and Applied Optimization, Graduate School of Information Technology & Mathematical Sciences, University of Ballarat, Ballarat, Australia 3353;Center for General Education, Kaohsiung Medical University, Kaohsiung, Taiwan 80708
Venue:
Journal of Global Optimization
Year:
2011

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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 Fr茅chet 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.