An Implicit-Function Theorem for B-Differentiable Functions

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3184 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3184 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3184 archive 351 disk0/00/00/31/38 2016-01-15 01:58:58 2021-08-27 17:13:16 2016-01-15 01:58:58 monograph show 2 Robinson S.M. An Implicit-Function Theorem for B-Differentiable Functions pub iis_met prog_ado A function from one normed linear space to another is said to be Bouligand differentiable (B-differentiable) at a point if it is directionally differentiable there in every direction, and if the directional derivative has a certain uniformity property. This is a weakening of the classical idea of Frechet (F-) differentiability, and it is useful in dealing with optimization problems and in other situations in which F-differentiability may be too strong. In this paper we introduce a concept of strong B-derivative, and we employ this idea to prove an implicit-function theorem for B-differentiable functions. This theorem provides the same kinds of information as does the classical implicit-function theorem, but with B-differentiability in place of F-differentiability. Therefore it is applicable to a considerably wider class of functions than is the classical theorem. 1988-07 published WP-88-067 WP-88-067 10 public working_paper IIASA, Laxenburg, Austria 19 FALSE info:eu-repo/semantics/book