Set-Valued Analysis

, Volume 3, Issue 3, pp 213–261 | Cite as

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

  • Zvi Artstein
Article

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.

Mathematics Subject Classifications (1991)

26E25 34G20 54C60 58C06 

Key words

set-valued maps set-valued calculus set-valued evolution equations 

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Zvi Artstein
    • 1
  1. 1.Department of Theoretical MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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