eprintid: 14127
rev_number: 7
eprint_status: archive
userid: 5
dir: disk0/00/01/41/27
datestamp: 2016-12-12 15:33:37
lastmod: 2021-08-27 17:41:43
status_changed: 2016-12-12 15:33:37
type: book_section
metadata_visibility: show
item_issues_count: 1
creators_name: Demidova, V. A.
creators_name: Demyanov, V.F.
creators_id: AL1612
title: A directional implicit function theorem for quasidifferentiable functions
ispublished: pub
divisions: prog_sds
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).
date: 1986
date_type: published
publisher: Springer Berlin Heidelberg
id_number: doi:10.1007/BFb0121140
creators_browse_id: 2579
creators_browse_id: 2579
full_text_status: none
series: Mathematical Programming Studies
volume: 29
place_of_pub: Germany
pagerange: 95-107
refereed: TRUE
isbn: 978-3-642-00929-7
issn: 0303-3929
book_title: Quasidifferential Calculus
editors_name: Demyanov, V. F.
editors_name: Dixon, L.C.W.
editors_id: AL1612
coversheets_dirty: FALSE
fp7_type: info:eu-repo/semantics/bookPart
citation:   Demidova, V. A. & Demyanov, V.F. <https://pure.iiasa.ac.at/view/iiasa/2579.html>  (1986).  A directional implicit function theorem for quasidifferentiable functions.    In:  Quasidifferential Calculus. Eds. Demyanov, V. F. <https://pure.iiasa.ac.at/view/iiasa/2579.html> & Dixon, L.C.W., pp. 95-107 Germany: Springer Berlin Heidelberg.  ISBN 978-3-642-00929-7 10.1007/BFb0121140 <https://doi.org/10.1007/BFb0121140>.