Ekeland, I. (Ivar) 1944
Overview
Works:  160 works in 543 publications in 13 languages and 9,710 library holdings 

Genres:  Conference papers and proceedings Juvenile works History 
Roles:  Author, Editor, Publishing director, Author of introduction, Thesis advisor, Author of afterword, colophon, etc., Contributor, Director, Interviewee, Honoree, Other 
Classifications:  QA614.58, 514.7 
Publication Timeline
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Most widely held works by
I Ekeland
Mathematics and the unexpected by
I Ekeland(
Book
)
49 editions published between 1984 and 2001 in 7 languages and held by 1,573 WorldCat member libraries worldwide
In this brief treatise, Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project, but particulars are practically impossible
49 editions published between 1984 and 2001 in 7 languages and held by 1,573 WorldCat member libraries worldwide
In this brief treatise, Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project, but particulars are practically impossible
The broken dice, and other mathematical tales of chance by
I Ekeland(
Book
)
13 editions published between 1991 and 1996 in English and French and held by 980 WorldCat member libraries worldwide
13 editions published between 1991 and 1996 in English and French and held by 980 WorldCat member libraries worldwide
The best of all possible worlds : mathematics and destiny by
I Ekeland(
Book
)
9 editions published between 2006 and 2007 in English and held by 775 WorldCat member libraries worldwide
Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what "is" the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of "optimization," or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of eruditionone that will be essential reading for popularscience buffs and historians of science alike
9 editions published between 2006 and 2007 in English and held by 775 WorldCat member libraries worldwide
Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what "is" the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of "optimization," or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of eruditionone that will be essential reading for popularscience buffs and historians of science alike
Applied nonlinear analysis by
Jean Pierre Aubin(
Book
)
24 editions published between 1984 and 2006 in 4 languages and held by 577 WorldCat member libraries worldwide
24 editions published between 1984 and 2006 in 4 languages and held by 577 WorldCat member libraries worldwide
Convex analysis and variational problems by
I Ekeland(
Book
)
37 editions published between 1976 and 1999 in 4 languages and held by 543 WorldCat member libraries worldwide
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). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references
37 editions published between 1976 and 1999 in 4 languages and held by 543 WorldCat member libraries worldwide
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). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references
The cat in numberland by
I Ekeland(
Book
)
7 editions published between 2006 and 2014 in 3 languages and held by 432 WorldCat member libraries worldwide
Brings number concepts to life for all ages
7 editions published between 2006 and 2014 in 3 languages and held by 432 WorldCat member libraries worldwide
Brings number concepts to life for all ages
Convexity methods in Hamiltonian mechanics by
I Ekeland(
Book
)
18 editions published between 1989 and 2012 in English and Undetermined and held by 414 WorldCat member libraries worldwide
In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the threebody problem in celestial mechanics, they are found by perturbation theory: there is a small parameter € in the problem, the mass of the perturbing body for instance, and for € = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for € # 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an areapreserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods
18 editions published between 1989 and 2012 in English and Undetermined and held by 414 WorldCat member libraries worldwide
In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the threebody problem in celestial mechanics, they are found by perturbation theory: there is a small parameter € in the problem, the mass of the perturbing body for instance, and for € = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for € # 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an areapreserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods
Infinitedimensional optimization and convexity by
I Ekeland(
Book
)
11 editions published in 1983 in English and held by 306 WorldCat member libraries worldwide
The caratheodory approach; Infinitedimensional optimization; Duality theory
11 editions published in 1983 in English and held by 306 WorldCat member libraries worldwide
The caratheodory approach; Infinitedimensional optimization; Duality theory
Mathematical techniques of optimization, control, and decision by
Jean Pierre Aubin(
Book
)
11 editions published between 1981 and 1983 in 4 languages and held by 251 WorldCat member libraries worldwide
11 editions published between 1981 and 1983 in 4 languages and held by 251 WorldCat member libraries worldwide
Advances in Hamiltonian systems by
Istituto matematico Guido Castelnuovo(
Book
)
11 editions published in 1983 in English and held by 221 WorldCat member libraries worldwide
11 editions published in 1983 in English and held by 221 WorldCat member libraries worldwide
Analyse convexe et problèmes variationnels by
I Ekeland(
Book
)
10 editions published in 1974 in French and Undetermined and held by 207 WorldCat member libraries worldwide
10 editions published in 1974 in French and Undetermined and held by 207 WorldCat member libraries worldwide
Variational methods : proceedings of a conference, Paris, June 1988 by
H Berestycki(
Book
)
9 editions published in 1990 in English and held by 180 WorldCat member libraries worldwide
In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap plications from various domains of sciences and industrial applica tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics
9 editions published in 1990 in English and held by 180 WorldCat member libraries worldwide
In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap plications from various domains of sciences and industrial applica tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics
Au hasard : la chance, la science et le monde by
I Ekeland(
Book
)
16 editions published between 1991 and 2015 in 3 languages and held by 167 WorldCat member libraries worldwide
Une étude sur le hasard et les rapports que la science entretient avec la chance, s'appuyant sur des épisodes de Les Sagas des rois de Norvège, de S. Sturlasson. Chacun de ces épisodes sert de point de départ à un développement philosophique
16 editions published between 1991 and 2015 in 3 languages and held by 167 WorldCat member libraries worldwide
Une étude sur le hasard et les rapports que la science entretient avec la chance, s'appuyant sur des épisodes de Les Sagas des rois de Norvège, de S. Sturlasson. Chacun de ces épisodes sert de point de départ à un développement philosophique
Elements d'economie mathematique by
I Ekeland(
Book
)
13 editions published in 1979 in 3 languages and held by 154 WorldCat member libraries worldwide
13 editions published in 1979 in 3 languages and held by 154 WorldCat member libraries worldwide
Le chaos : un exposé pour comprendre : un essai pour réfléchir by
I Ekeland(
Book
)
17 editions published between 1995 and 2010 in 4 languages and held by 147 WorldCat member libraries worldwide
Explique la théorie du chaos et ses conséquences mécaniques et astronomiques. L'auteur propose ensuite une réflexion sur l'existence de l'autonomie des objets mathématiques et sur la précision fluctuante des calculs humains face à une nature bien plus complexe qu'on ne l'imagine
17 editions published between 1995 and 2010 in 4 languages and held by 147 WorldCat member libraries worldwide
Explique la théorie du chaos et ses conséquences mécaniques et astronomiques. L'auteur propose ensuite une réflexion sur l'existence de l'autonomie des objets mathématiques et sur la précision fluctuante des calculs humains face à une nature bien plus complexe qu'on ne l'imagine
La theorie des jeux et ses applications a l'economie mathematique by
I Ekeland(
Book
)
10 editions published in 1974 in French and English and held by 131 WorldCat member libraries worldwide
10 editions published in 1974 in French and English and held by 131 WorldCat member libraries worldwide
L'idée du service public estelle encore soutenable? : [actes du colloque, octobre 1997, Université de ParisDauphine](
Book
)
5 editions published in 1999 in French and held by 98 WorldCat member libraries worldwide
5 editions published in 1999 in French and held by 98 WorldCat member libraries worldwide
Le meilleur des mondes possibles : mathématiques et destinée by
I Ekeland(
Book
)
7 editions published between 2000 and 2004 in French and Finnish and held by 89 WorldCat member libraries worldwide
La théorie du chaos a attiré l'attention sur ce qu'il y a d'imprévisible et de hasardeux dans les lois de la physique. Une très ancienne théorie philosophique affirme au contraire l'harmonie générale de l'univers, Leibniz parle même du meilleur des mondes possibles. L'auteur retrace l'histoire de cette idée et montre les résultats scientifiques sur lesquels elle s'appuie
7 editions published between 2000 and 2004 in French and Finnish and held by 89 WorldCat member libraries worldwide
La théorie du chaos a attiré l'attention sur ce qu'il y a d'imprévisible et de hasardeux dans les lois de la physique. Une très ancienne théorie philosophique affirme au contraire l'harmonie générale de l'univers, Leibniz parle même du meilleur des mondes possibles. L'auteur retrace l'histoire de cette idée et montre les résultats scientifiques sur lesquels elle s'appuie
Nonlinear functional analysis and applications to differential equations : proceedings of the second school, ICTP, Trieste,
Italy, 21 April9 May 1997(
Book
)
4 editions published in 1998 in English and held by 71 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 71 WorldCat member libraries worldwide
Identification and estimation of hedonic models by
I Ekeland(
Book
)
21 editions published between 2002 and 2003 in English and held by 70 WorldCat member libraries worldwide
This paper considers the identification and estimation of hedonic models. We establish that in an additive version of the hedonic model, technology and preferences are generically identified up to affine transformations from data on demand and supply in a single hedonic market. For a very general parametric structure preferences and technology are fully identified. This is true under a strong assumption of statistical independence of the error term. It is also true under the weaker assumption of mean independence of the error term. Much of the confusion in the empircial literature that claims that hedonic models estimated on data from a single market are fundamentally underidentified is based on linearizations that do not use all of the information in the model. The exact economic model that justifies widely used linear approximations has strange properties so the approximation is doubly poor. A semiparametric estimation method is proposed that is valid when a statistical independence assumption is valid. Alternatively, under the weaker condition of mean independence instrumental variables estimators can be applied to identify technology and preference parameters from a single market. They are justified by nonlinearities that are generic features of equilibrium in hedonic models
21 editions published between 2002 and 2003 in English and held by 70 WorldCat member libraries worldwide
This paper considers the identification and estimation of hedonic models. We establish that in an additive version of the hedonic model, technology and preferences are generically identified up to affine transformations from data on demand and supply in a single hedonic market. For a very general parametric structure preferences and technology are fully identified. This is true under a strong assumption of statistical independence of the error term. It is also true under the weaker assumption of mean independence of the error term. Much of the confusion in the empircial literature that claims that hedonic models estimated on data from a single market are fundamentally underidentified is based on linearizations that do not use all of the information in the model. The exact economic model that justifies widely used linear approximations has strange properties so the approximation is doubly poor. A semiparametric estimation method is proposed that is valid when a statistical independence assumption is valid. Alternatively, under the weaker condition of mean independence instrumental variables estimators can be applied to identify technology and preference parameters from a single market. They are justified by nonlinearities that are generic features of equilibrium in hedonic models
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Related Identities
 Aubin, Jean Pierre Author Editor
 Temam, Roger Contributor
 Bensoussan, Alain Editor
 Turnbull, Thomas
 C.E.R.E.M.A.D.E.
 Istituto matematico Guido Castelnuovo
 Berestycki, H. (Henri) Author Editor
 Coron, JeanMichel 1956 Editor
 Centre national de la recherche scientifique (France)
 FrisonRoche, MarieAnne Publishing director Director
Useful Links
Associated Subjects
Calculus of variations Catastrophes (Mathematics) Chaotic behavior in systems Control theory Convex domains Convex functions Decision making Differentiable dynamical systems Differential equations, Elliptic Differential equations, Nonlinear Differential equations, Partial Econometric models Econometrics Economics, Mathematical Ethics EuropeEuropean Union countries Game theory Global analysis (Mathematics) Government business enterprises Hamiltonian systems Harmony (Philosophy) Human behavior Infinite Logic, Symbolic and mathematical Mathematical analysis Mathematical optimization Mathematical statistics Mathematics MathematicsPhilosophy Nonlinear functional analysis Number concept Number conceptStudy and teaching Parameter estimation Probabilities Science ScienceMathematics SciencePhilosophy System theory United States
Alternative Names
Ekeland, I.
Ekeland, I. 1944
Ekeland, I. (Ivar)
Ekeland, Ivar.
Ekeland, Ivar 1944
Èkland, I.
Ėkland, I. 1944
Ėkland, Ivar 1944
Ivar Ekeland Frans wiskundige
Ivar Ekeland fransk matematikar
Ivar Ekeland fransk matematiker
Ivar Ekeland französischer Mathematiker
Ivar Ekeland French mathematician
Ivar Ekeland matemático francés
Ivar Ekeland mathématicien français
Экланд, И 1944
에클랑, 이바르 1944
イヴァール・エクランド
エクランド, イーヴァル
Languages
English
(173)
French (81)
Italian (10)
Spanish (8)
German (7)
Finnish (3)
Russian (3)
Chinese (3)
Polish (2)
Greek, Modern (2)
Dutch (1)
Norwegian (1)
Czech (1)
French (81)
Italian (10)
Spanish (8)
German (7)
Finnish (3)
Russian (3)
Chinese (3)
Polish (2)
Greek, Modern (2)
Dutch (1)
Norwegian (1)
Czech (1)
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