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Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization

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Abstract

We consider sensitivity analysis in terms of variational sets for nonsmooth vector optimization. First, relations between variational sets, or their minima/weak minima, of a set-valued map and that of its profile map are obtained. Second, given an objective map, relationships between the above sets of this objective map and that of the perturbation map and weak perturbation map are established. Finally, applications to constrained vector optimization are given. Many examples are provided to illustrate the essentialness of the imposed assumptions and some advantages of our results.

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Acknowledgements

This research was supported by the Vietnam National University Hochiminh City. A part of the work of the second author was completed during his stay as a visiting professor at the Vietnam Institute for Advanced Study in Mathematics, whose hospitality is gratefully acknowledged. The authors are indebted to an anonymous referee for many valuable detailed remarks which have helped improve the paper significantly.

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Authors and Affiliations

  1. Department of Mathematics and Computing, University of Science of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam

    N. L. H. Anh

  2. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    P. Q. Khanh

Authors
  1. N. L. H. Anh
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  2. P. Q. Khanh
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Correspondence to N. L. H. Anh.

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Communicated by Stefan Rolewicz.

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Anh, N.L.H., Khanh, P.Q. Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization. J Optim Theory Appl 158, 363–384 (2013). https://doi.org/10.1007/s10957-012-0257-5

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  • DOI: https://doi.org/10.1007/s10957-012-0257-5

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