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Wednesday, November 18, 2020 | History

3 edition of Ekeland variational principle found in the catalog.

Ekeland variational principle

Irina Meghea

Ekeland variational principle

with generalizations and variants

by Irina Meghea

  • 216 Want to read
  • 40 Currently reading

Published by EAC, Éd. des Archives Contemporaines, Old City Pub. in Paris, Philadelphia (Pa) .
Written in English

  • Metric spaces,
  • Calculus of variations,
  • Banach spaces

  • Edition Notes

    Includes bibliographical references and index.

    StatementIrina Meghea
    LC ClassificationsQA315 .M43 2009
    The Physical Object
    Paginationiv, 524 p. :
    Number of Pages524
    ID Numbers
    Open LibraryOL25253863M
    ISBN 102914610963, 1933153083
    ISBN 109782914610964, 9781933153087
    LC Control Number2012360682

    Some new vectorial Ekeland variational principles in cone quasi-uniform spaces are proved. Some new equivalent principles, vectorial quasivariational inclusion principle, vectorial quasi-optimization principle, vectorial quasiequilibrium principle are obtained. Also, several other important principles in nonlinear analysis are extended to cone quasi-uniform spaces. What is the difference between Deformation technique and Ekeland's variational principle to approach Mountain Pass theorem? Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

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Ekeland variational principle by Irina Meghea Download PDF EPUB FB2

The Ekeland variational principle, formulated by Ivar Ekeland inis the foundation of modern variational calculus. Among its findings there are numerous and various applications which are developed and described in Ekeland Variational Principle with Variants and Generalizations. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATI () On the Variational Principle I.

EKELAND VER Mathématiques de la Décision, Université Paris IX, Pa France Submitted by J. Lions The variational principle states that if a differentiable functional F attains its minimum at some point u, then F'(u) = 0; it has proved a valuable tool for Cited by: Lin, L.J., Chuang, C.S.: Existence theorems for variational inclusion problems and the set-valued vector Ekeland variational principle in a complete metric space.

Nonlinear Anal. 70(7), – () MathSciNet CrossRef zbMATH Google ScholarCited by: 3. In this work, we investigate the modular version of the Ekeland variational principle (EVP) in the context of variable exponent sequence spaces ℓ p (). The core obstacle in the development of a modular version of the EVP is the failure of the triangle inequality for the module.

It is the lack of this inequality, which is indispensable in the establishment of the classical EVP, that has. Since its appearance in the variational principle of Ekeland has found many applications in different fields in Analysis. The best refer-ences for those are by Ekeland himself: his survey article [23] and his book with J.-P.

Aubin [2]. Not all material presented here appears in those places. Some are scattered around and there lies my. On the Variational Principle I. EKELAND UER Mathe’matiques de la DC&ion, Waiver& Paris IX, Pa France Submitted by J.

Lions The variational principle states that if a differentiable functional F attains its minimum at some point zi, then F’(C) = 0; it has proved a valuable tool for.

Looking at the many applications of the Ekeland Variational Principle, some 2 years ago we met the Mountain Pass Theorem of Ambrosetti—Rabinowitz.

This stimulated us to know more about Critical Point Theory, and to better understand the fascinating interplay between the topological and differential ideas of the minimax approach.

variational principles led to the relaxation of the compactness assumptions. Such principles typically assert that any lower semicontinuous (lsc) function, bounded from below, may be perturbed slightly to ensure the existence of the. The Ekeland variational principle in nonsmooth critical point theory has already been used in earlier papers as, for instance, in.

Now, we present the main result of this paper. Theorem Let X be a real Banach space and let Φ, Ψ: X → R be two continuously Gâteaux differentiable functions. On the variational principle (Charles University, Prague) [pdf] Adverse selection and optimal transportation: a Ekeland variational principle book history (TSE, in honor of Jean-Jacques Laffont) Optimal pits and optimal transportation.

John Forbes Nash, Ekeland variational principle book. () and. Abstract: We present two existence principles for minimal points of subsets of the product space X × 2 Y, where X stands for a separated uniform space and Y a topological vector space.

The two principles are distinct with respect to the involved ordering structure in 2 Y. We derive from them new variants of Ekeland's principle for set-valued maps as well as a minimal point theorem in X × Y.

A variational principle is a scientific principle used within the calculus of variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those example, to answer this question: "What is Ekeland variational principle book shape of a chain suspended at both ends?" we can use the variational principle that the shape must minimize the.

The emphasis in this book is on the new developments tions, one often needs to combine a variational principle. Introduction 5 mple,adecouplingmethod that mimics in nonconvex settings the role of Fenchel du- Ekeland Variational Principles. By using the concept of Γ-distance, we prove EVP (Ekeland’s variational principle) on quasi-F-metric (q-F-m) spaces.

We apply EVP to get the existence of the solution to EP (equilibrium problem) in complete q-F-m spaces with Γ-distances. Also, we generalize Nadler’s fixed point theorem.

Variational Methods: Proceedings of a Conference Paris, June Birkhäuser Basel Frederick J. Almgren Jr., Elliott H. Lieb (auth.), Henri Berestycki, Jean-Michel Coron, Ivar Ekeland (eds.).

Ekeland is known as the author of Ekeland's variational principle and for his use of the Shapley–Folkman lemma in optimization theory. He has contributed to the periodic solutions of Hamiltonian systems and particularly to the theory of Kreĭn indices for linear systems (Floquet theory).

Try the new Google Books. Check out the new look and enjoy easier access to your favorite features. Try it now. No thanks. Try the new Google Books View eBook. Get this book in print 22 Ekeland variational principle.

23 General minimax principle. 24 Semilinear Dirichlet problem. 25 Location theorem. 26 Critical. No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension).Reviews: 1.

The Ekeland variational principle is a general minimization result with a broad variety of applications. It provides a specific method in choosing a minimizing sequence; consequently, this minimizing sequence along with some other conditions give rise to numerous applications.

I'm looking for geometric applications of Ekeland's variational principle in order to see it at work in a context I'm familiar with. in the book of Borwein & Lewis (Convex Analysis and Nonlinear Optimization) pagethey use the PVE to prove that every Chebyshev set (i.e.

every set that has the property "every point has a unique nearest. Ekeland’s variational principle has many generalizations, see [23], [24] and the very recent books of Borwein and Zhu [10], Meghea [21] and their references.

Ekeland’s variational principle is. P A R T I: Variational Principles in Mathematical Physics 1 1 Variational Principles 2 Minimization techniques and Ekeland variational principle 2 Borwein-Preiss variational principle 8 Minimax principles 12 Mountain pass type results 12 Minimax results via Ljusternik-Schnirelmann category 15 Ricceri’s variational.

"This book maps the progress that has been made since the publication of the Ekeland variational principle in in the development and application of the variational approach in nonlinear analysis. The authors are well equipped for their task. The Ekeland’s variational principle, see [1], allows for each ε > 0, each δ > 0 and each x ∈ E such as Φ(x) ≤ inf E Φ+ε, to build an element v ∈ E minimizing the functional Φ v given by Φ v(x) = Φ(x)+ ε δ d(x,v).

This principle has wide applications in optimization and nonlinear analysis [1, 2, 4]. Ekeland has contributed to mathematical analysis, particularly to variational calculus and mathematical optimization.

Variational principle. In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist a nearly optimal solution to a class of optimization problems.

Lectures on the Ekeland variational principle with applications and detours. Berlin ; New York: Published for the Tata Institute of Fundamental Research [by] Springer-Verlag, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Djairo Guedes de Figueiredo.

Lectures on the Ekeland variational principle with applications and detours. [Djairo Guedes de Figueiredo] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Book\/a>, schema:CreativeWork\/a> ; \u00A0\u00A0\u00A0\n library.

We consider a distance function on generalized metric spaces and we get a generalization of Ekeland Variational Principle (EVP). Next, we prove that EVP is equivalent to Caristi–Kirk fixed point theorem and minimization Takahashi’s theorem. parabolic equations, pointwise state constraints, optimal control, Pontryagin maximum principle, Ekeland variational principle AMS Subject Headings 49K20, 35K10, 35K Addenda: The Ekeland Variational Principle / Proof of Brouwer's Fixed Point Theorem / Motzkin's Characterization of Convex Sets Corrections: The Thoughtful Correction of Footnote 47 by Douglas Bridges / Typos.

Chapter E: Continuity II Addenda Corrections. Chapter F: Linear Spaces Addenda Corrections: Typos. Chapter G: Convexity Addenda. Equivalents of Ekeland's principle - Volume 48 Issue 3 - W.

Oettli, M. Théra. To send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage.

THE EKELAND VARIATIONAL PRINCIPLE Arguing in a classical way of the smooth analysis (as, for instance, Ghossoub), but using the definitions and properties of the non-smooth analysis (as, for instance, Motreanu-Radulescu, the following consequence of the Ekeland variational Principle.

land’s variational principle has many generalizations in the very recent books of Borwein, Zhu [3], Meghea [7] and the references therein. In this paper we give a generalized form of Ekeland variational princi-ple, which is a generalization of the variational principles given by Ekeland-Borwein-Preiss and also by Zhong.

As a consequence, we. Ekeland variational principle [13][14][15] is one the most elegant and important results from nonlinear analysis and it has many applications in different areas of science, engineering, social.

In this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle.

The main tools used are the Ekeland's variational principle combined with penalization and spike variation techniques. In the proof of Ekeland's Variational Principle, as you mention, the closedness is used to invoke Cantor's Intersection Theorem, which states that a nested sequence of closed sets in a complete metric space whose diameter goes to zero must have a nonempty, singleton intersection.

The proof goes as follows: if $\{C_n\}$ is the nested sequence of. validity of Caristi fixed point theorem principle on the completeness of the underlying quasi-pseudometric space were studied as well. In [1] the same is done for the weak form of Ekeland variational principle and Takahashi minimization principle.

The extension of wEk to arbitrary quasi-metric spaces was given in [19]. Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems | Alexandru Kristály, Vicenţiu D.

Rădulescu, Csaba Varga | download | B–OK. Download books for free. Find books. It is shown that this condition is sufficient for a bounded below, lower semicontinuous function to attain its minimum. Criteria for a generalized Caristi-like condition to hold are derived. Generalizations of the Ekeland and Bishop--Phelps variational principles are obtained and compared with their prototypes.

Book Description. Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.

The book presents the most important variational methods for elliptic PDEs. Ekeland's variational principle. The following theorem will be of constant use throughout this monograph. The applications of this principle to non-linear analysis are numerous and well documented in several books ([A-E], [Ek 1], [De]).

Recommend this book.Infinite-Dimensional Optimization and Convexity [Ivar Ekeland and Thomas Turnbull]. In this volume, Ekeland and Turnbull are mainly concerned with existence theory. They seek to determine whether, when given an optimization problem consisting of mini.().

Vectorial form of Ekeland variational principle with applications to vector equilibrium problems. Optimization: Vol. 69, No. 3, pp.