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A calculus for set-valued maps and set-valued evolution equations

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Abstract

A definition of differentiability of a set-valued map is offered. As derivatives, which are called directives in the set-valued setting, unions of affine maps are used; these are called multiaffines. A multiaffine is a directive if it is a first-order approximation of the set-valued map. One application is a necessary condition for maximin optimality of constrained decisions. A distance among multiaffines permits the development of set-valued evolution equations along the lines of ordinary differential equations in a vector space. The theory is displayed along with some comments on applications.

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  1. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Zvi Artstein

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  1. Zvi Artstein
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Incumbent of the Hettie H. Heineman Professorial Chair in Mathematics.

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Artstein, Z. A calculus for set-valued maps and set-valued evolution equations. Set-Valued Anal 3, 213–261 (1995). https://doi.org/10.1007/BF01025922

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