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Codifferential Calculus

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Abstract

In this paper, some exact calculus rules are obtained for calculating the coderivatives of the composition of two multivalued maps. Similar rules are displayed for sums. A crucial role is played by an intermediate set-valued map called the resolvent. We first establish inclusions for contingent, Fréchet and limiting coderivatives. Combining them, we get equality rules. The qualification conditions we present are natural and less exacting than classical conditions.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Shengjie Li & Xiaowei Xue

  2. Laboratoire de Mathématiques Appliquées, UMR CNRS 5142, Faculté des Sciences, Université de Pau et des Pays de l’Adour, B.P. 1155, 64013, Pau Cedex, France

    Jean-Paul Penot

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  1. Shengjie Li
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  2. Jean-Paul Penot
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Correspondence to Shengjie Li.

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

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Li, S., Penot, JP. & Xue, X. Codifferential Calculus. Set-Valued Anal 19, 505–536 (2011). https://doi.org/10.1007/s11228-010-0171-7

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