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Approximate subdifferentials and applications 3: the metric theory

Published online by Cambridge University Press:  26 February 2010

A. D. Ioffe
A. D. Ioffe
Affiliation:
Department of Mathematics, Technion, Haifa, Israel.
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Extract

This is the final paper of the series of three papers under the same title. The finite dimensional theory developed in the first of them 7 contains first of all:

(a) a calculus having among its consequences the calculi of convex subdifferentials and generalized gradients of Clarke (henceforth sometimes abbreviated C.g.g.) in the most general form which is partly due to the fact that in a finite dimensional space

for any convex function f and

for any SX (A means approximate, C means Clarke); and (b) a theorem stating that approximate subdifferentials are minimal (as sets) among all possible subdifferentials satisfying one or another set of conditions (usually very natural).

Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 1 - 38
Copyright
Copyright University College London 1989

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