Robinson, S.M.
(1988).
*An Implicit-Function Theorem for B-Differentiable Functions.*
IIASA Working Paper.
IIASA, Laxenburg, Austria: WP-88-067

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## Abstract

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.

Item Type: | Monograph (IIASA Working Paper) |
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Research Programs: | Adaption and Optimization (ADO) |

Depositing User: | IIASA Import |

Date Deposited: | 15 Jan 2016 01:58 |

Last Modified: | 27 Aug 2021 17:13 |

URI: | https://pure.iiasa.ac.at/3138 |

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