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Derivatives of the Efficient Point Multifunction in Parametric Vector Optimization Problems

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Abstract

In this paper, we deal with the sensitivity analysis in vector optimization. More specifically, formulae for inner and outer evaluating the S-derivative of the efficient point multifunction in parametric vector optimization problems are established. These estimating formulae are presented via the set of efficient/weakly efficient points of the S-derivative of the original multifunction, a composite multifunction of the objective function and the constraint mapping. The elaboration of the formulae in vector optimization problems, having multifunction constraints and semiinfinite constraints, is also undertaken. Furthermore, examples are provided for analyzing and illustrating the obtained results.

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Acknowledgements

This work was supported in part by the project “Joint research and training on Variational Analysis and Optimization Theory, with oriented applications in some technological areas” (Vietnam–USA). The author thanks an anonymous referee for valuable comments and suggestions which improved the original presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics & Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Hochiminh City, Vietnam

    Thai Doan Chuong

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  1. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

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Communicated by Nguyen Dong Yen.

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Chuong, T.D. Derivatives of the Efficient Point Multifunction in Parametric Vector Optimization Problems. J Optim Theory Appl 156, 247–265 (2013). https://doi.org/10.1007/s10957-012-0099-1

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