A directional implicit function theorem for quasidifferentiable functions

Demidova V A & Demyanov VF (1986). A directional implicit function theorem for quasidifferentiable functions. In: Quasidifferential Calculus. Eds. Demyanov, V. F. & Dixon, L.C.W., pp. 95-107 Germany: Springer Berlin Heidelberg. ISBN 978-3-642-00929-7 DOI:10.1007/BFb0121140.

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Abstract

The implicit and inverse function theorems provide an essential component of classical differential calculus, and for this reason many attempts have been made to extend these theorems to nonsmooth analysis (see, for example, the work of F. Clarke, H. Halkin, J.-B. Hiriart-Urruty, A.D. Ioffe, B.H. Pourciau, J. Warga). In this paper, we consider the case of quasidifferentiable functions. It is shown that to obtain nontrivial results it is necessary to study a directional implicit function problem (it turns out that in some directions there are several functions, while in others there are none).

Item Type: Book Section
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: Romeo Molina
Date Deposited: 12 Dec 2016 15:33
Last Modified: 02 May 2017 12:46
URI: http://pure.iiasa.ac.at/14127

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