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Higher-order generalized tangent epiderivatives and applications to set-valued optimization

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Abstract

In the paper, we introduce two new concepts on differentiability for set-valued maps, named by the higher-order generalized tangent epiderivative and the higher-order weak tangent epiderivative. Then, we study some basic properties and calculus rules for these notions. Finally, we mention their applications to two topics in set-valued optimization: optimality conditions and sensitivity analysis. More precisely, optimality conditions for some particular optimization problems are established and sensitivity analysis for the solution map of the parametric inclusion is given using higher-order generalized (weak) tangent epiderivatives. Several examples are proposed to illustrate the obtained results.

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Acknowledgements

Vo Duc Thinh was funded by Vingroup Joint Stock Company and supported by the Domestic Master/ PhD Scholarship Programme of Vingroup Innovation Foundation (VINIF), Vingroup Big Data Institute (VINBIGDATA), code VINIF.2020.TS.90.

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Authors and Affiliations

  1. Department of Optimization and System Theory, University of Science, Hochiminh City, Vietnam

    Nguyen Le Hoang Anh & Vo Duc Thinh

  2. Vietnam National University, Hochiminh City, Vietnam

    Nguyen Le Hoang Anh & Vo Duc Thinh

  3. Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam

    Vo Duc Thinh

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  1. Nguyen Le Hoang Anh
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  2. Vo Duc Thinh
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Correspondence to Nguyen Le Hoang Anh.

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Anh, N.L.H., Thinh, V.D. Higher-order generalized tangent epiderivatives and applications to set-valued optimization. Positivity 26, 87 (2022). https://doi.org/10.1007/s11117-022-00953-7

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