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Lectures on the ekeland variational principle with applications and detours

Lectures on the ekeland variational principle with applications and detours Acta Applicandae Mathematicae 24: (1991). 195 Book Reviews D. G. de Figueiredo: Lectures on The Ekeland Variational Principle with Applications and Detours, Tata Institute of Fundamental Research, Bombay, Lectures on Mathematics and Physics-Mathematics 81, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1989, 96 pp., Softcover DM20,-, ISBN 3-540-51179-2. This monograph is devoted to explaining the Ekeland variational principle (EVP) and its applications. Since its appearance in 1972, this principle has found many applications in different fields of analysis. The most general version of the EVP presented in these notes is the following: Let (X, d) be a complete metric space. Let O: X ~ R w { +~} be a lower semicontinuous function which is bounded below. Let e > 0 and ft~X be given such that O(fi) ~< infx • + e/2. Then, #iven 2 > 0, there exists u~ ~ X such that O(uz) ~< O(fi), d(u~, ~) <~ 2, @(uz) < O(u) + -2 d(u, u~t) , Vu ~ u;~. In Chapter 1, the notions of lower semicontinuity (1.s.c.) and sequential lower semicontinuity are introduced and relations between them are studied. The well- known theorem about the existence of the minimizing point of a 1.s.c. functional over http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Lectures on the ekeland variational principle with applications and detours

Acta Applicandae Mathematicae , Volume 24 (2) – May 1, 2004

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References (29)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00046892
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 24: (1991). 195 Book Reviews D. G. de Figueiredo: Lectures on The Ekeland Variational Principle with Applications and Detours, Tata Institute of Fundamental Research, Bombay, Lectures on Mathematics and Physics-Mathematics 81, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1989, 96 pp., Softcover DM20,-, ISBN 3-540-51179-2. This monograph is devoted to explaining the Ekeland variational principle (EVP) and its applications. Since its appearance in 1972, this principle has found many applications in different fields of analysis. The most general version of the EVP presented in these notes is the following: Let (X, d) be a complete metric space. Let O: X ~ R w { +~} be a lower semicontinuous function which is bounded below. Let e > 0 and ft~X be given such that O(fi) ~< infx • + e/2. Then, #iven 2 > 0, there exists u~ ~ X such that O(uz) ~< O(fi), d(u~, ~) <~ 2, @(uz) < O(u) + -2 d(u, u~t) , Vu ~ u;~. In Chapter 1, the notions of lower semicontinuity (1.s.c.) and sequential lower semicontinuity are introduced and relations between them are studied. The well- known theorem about the existence of the minimizing point of a 1.s.c. functional over

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 1, 2004

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