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Calculus Rules for Derivatives of Multimaps

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Abstract

In this paper, by virtue of two intermediate derivative-like multifunctions, which depend on an element in the intermediate space, some exact calculus rules are obtained for calculating the derivatives of the composition of two set-valued maps. Similar rules are displayed for sums. Moreover, by using these calculus rules, the solution map of a parametrized variational inequality and the variations of the feasible set of a parametrized mathematical programming problem are studied.

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Authors and Affiliations

  1. College of Mathematics and Science, Chongqing University, Chongqing, 400044, China

    S. J. Li & K. W. Meng

  2. Dpartement de Mathmatiques Appliques, Facult des Sciences, Av. de l’Universit, 64000, Pau Cedex, France

    J.-P. Penot

  3. Laboratoire de Mathmatiques Appliques, Universit de Pau, UMR CNRS, 5142, France

    J.-P. Penot

Authors
  1. S. J. Li
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  2. K. W. Meng
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  3. J.-P. Penot
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Correspondence to S. J. Li.

Additional information

This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 60574073).

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Li, S.J., Meng, K.W. & Penot, JP. Calculus Rules for Derivatives of Multimaps. Set-Valued Anal 17, 21–39 (2009). https://doi.org/10.1007/s11228-009-0105-4

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  • DOI: https://doi.org/10.1007/s11228-009-0105-4

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