Obratnye funktsii i printsipy sushestvovaniya

Jan Brinkhuis

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Each one of six general existence principles---of compactness (the extreme value theorem), completeness (the Newton method or the modified Newton method), topology (Brouwer's fixed point theorem), homotopy (on contractions of a sphere to its center), variational analysis (Ekeland's principle) and monotonicity (the theorem of Minty-Browder)---is shown to lead to the inverse function theorem---some of which have been constructed specially for this paper---each one giving some novel insight. There are differences in assumptions and algorithmic properties. Simple proofs of the last two principles are included. The proof by compactness is shorter and simpler than the shortest and simplest known proof, that by completion. This gives a very short self-contained proof of the Lagrange multiplier rule that depends only on optimization methods. The proofs are of independent interest and are intended as well to be useful in the context of the ongoing efforts to obtain new variants of methods that are based on the inverse function theorem, such as comparative statics methods.
Original languageUndefined/Unknown
Pages (from-to)35-47
Number of pages13
JournalFundamental and Applied Mathematics (FPM)
Volume19
Issue number5
Publication statusPublished - 2015

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