Aubin, Jean Pierre
Overview
Works:  188 works in 606 publications in 5 languages and 7,353 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Thesis advisor, Other 
Classifications:  QA371, 515.7 
Publication Timeline
.
Most widely held works by
Jean Pierre Aubin
Approximation of elliptic boundaryvalue problems by
Jean Pierre Aubin(
Book
)
30 editions published between 1972 and 2007 in 4 languages and held by 533 WorldCat member libraries worldwide
30 editions published between 1972 and 2007 in 4 languages and held by 533 WorldCat member libraries worldwide
Applied abstract analysis by
Jean Pierre Aubin(
Book
)
14 editions published in 1977 in English and Undetermined and held by 532 WorldCat member libraries worldwide
14 editions published in 1977 in English and Undetermined and held by 532 WorldCat member libraries worldwide
Differential inclusions : setvalued maps and viability theory by
Jean Pierre Aubin(
Book
)
15 editions published between 1984 and 2014 in English and held by 505 WorldCat member libraries worldwide
A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the setvalued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the righthand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E  A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable
15 editions published between 1984 and 2014 in English and held by 505 WorldCat member libraries worldwide
A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the setvalued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the righthand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E  A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable
Explicit methods of optimization by
Jean Pierre Aubin(
Book
)
27 editions published between 1982 and 1984 in 3 languages and held by 398 WorldCat member libraries worldwide
27 editions published between 1982 and 1984 in 3 languages and held by 398 WorldCat member libraries worldwide
Neural networks and qualitative physics by
Jean Pierre Aubin(
Book
)
15 editions published between 1994 and 2011 in English and held by 302 WorldCat member libraries worldwide
"This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. The rapid advances in these two areas have left unanswered several mathematical questions that should motivate and challenge mathematicians." "Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and setvalued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the backpropagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints." "Mathematical models involve many features of a problem that may not be relevant to its solution. Qualitative physics, however, deals with an imperfect knowledge of the problem model. It is therefore more suited to the study of expert systems, which are shallow models and do not require structural knowledge of the problem." "This book should be a valuable introduction to the field for researchers in neural networks and cognitive systems, and should help to expand the range of study for viability theorists."Jacket
15 editions published between 1994 and 2011 in English and held by 302 WorldCat member libraries worldwide
"This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. The rapid advances in these two areas have left unanswered several mathematical questions that should motivate and challenge mathematicians." "Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and setvalued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the backpropagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints." "Mathematical models involve many features of a problem that may not be relevant to its solution. Qualitative physics, however, deals with an imperfect knowledge of the problem model. It is therefore more suited to the study of expert systems, which are shallow models and do not require structural knowledge of the problem." "This book should be a valuable introduction to the field for researchers in neural networks and cognitive systems, and should help to expand the range of study for viability theorists."Jacket
Dynamics of macrosystems : proceedings of a Workshop on the Dynamics of Macrosystems held at the International Institute for
Applied Systems Analysis (IIASA), Laxenburg, Austria, September 37, 1984 by
Jean Pierre Aubin(
Book
)
20 editions published between 1984 and 1987 in English and German and held by 279 WorldCat member libraries worldwide
20 editions published between 1984 and 1987 in English and German and held by 279 WorldCat member libraries worldwide
Convex analysis and optimization by
Jean Pierre Aubin(
Book
)
15 editions published between 1981 and 1982 in English and held by 274 WorldCat member libraries worldwide
15 editions published between 1981 and 1982 in English and held by 274 WorldCat member libraries worldwide
Mathematical techniques of optimization, control, and decision by
Jean Pierre Aubin(
Book
)
14 editions published between 1981 and 1983 in 4 languages and held by 267 WorldCat member libraries worldwide
14 editions published between 1981 and 1983 in 4 languages and held by 267 WorldCat member libraries worldwide
Viability theory by
Jean Pierre Aubin(
Book
)
27 editions published between 1991 and 2009 in English and Undetermined and held by 263 WorldCat member libraries worldwide
This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of firstorder partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplinesartificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciencesto go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis...The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially selfcontained. Bulletin of the AMS Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints. Mededelingen van het Wiskundig Genootschap
27 editions published between 1991 and 2009 in English and Undetermined and held by 263 WorldCat member libraries worldwide
This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of firstorder partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplinesartificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciencesto go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis...The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially selfcontained. Bulletin of the AMS Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints. Mededelingen van het Wiskundig Genootschap
Mathematical methods of game and economic theory by
Jean Pierre Aubin(
Book
)
6 editions published between 1979 and 2007 in English and held by 252 WorldCat member libraries worldwide
This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself
6 editions published between 1979 and 2007 in English and held by 252 WorldCat member libraries worldwide
This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself
Advances in Hamiltonian systems by
Istituto matematico Guido Castelnuovo(
Book
)
17 editions published in 1983 in English and Undetermined and held by 243 WorldCat member libraries worldwide
17 editions published in 1983 in English and Undetermined and held by 243 WorldCat member libraries worldwide
Analyse convexe et ses applications : comptes rendus, janvier 1974 by Conference sur analyse convexe et ses applications. Saint Pierre de Chartreuse(
Book
)
21 editions published in 1974 in 4 languages and held by 235 WorldCat member libraries worldwide
21 editions published in 1974 in 4 languages and held by 235 WorldCat member libraries worldwide
Dynamic economic theory : a viability approach by
Jean Pierre Aubin(
Book
)
14 editions published between 1997 and 2013 in English and held by 223 WorldCat member libraries worldwide
14 editions published between 1997 and 2013 in English and held by 223 WorldCat member libraries worldwide
Mutational and morphological analysis : tools for shape evolution and morphogenesis by
Jean Pierre Aubin(
Book
)
10 editions published between 1998 and 1999 in English and held by 183 WorldCat member libraries worldwide
The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory. These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth. However, shapes and images are basically sets, most often not smooth. J.P. Aubin thus constructs another vision, where shapes and images are just any compact set. Hence their evolution  which requires a kind of differential calculus  must be studied in the metric space of compact subsets. Despite the loss of linearity, one can transfer most of the basic results of differential calculus and differential equations in vector spaces to mutational calculus and mutational equations in any mutational space, including naturally the space of nonempty compact subsets. "Mutational and Morphological Analysis" offers a structure that embraces and integrates the various approaches, including shape optimization and mathematical morphology. Scientists and graduate students will find here other powerful mathematical tools for studying problems dealing with shapes and images arising in so many fields
10 editions published between 1998 and 1999 in English and held by 183 WorldCat member libraries worldwide
The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory. These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth. However, shapes and images are basically sets, most often not smooth. J.P. Aubin thus constructs another vision, where shapes and images are just any compact set. Hence their evolution  which requires a kind of differential calculus  must be studied in the metric space of compact subsets. Despite the loss of linearity, one can transfer most of the basic results of differential calculus and differential equations in vector spaces to mutational calculus and mutational equations in any mutational space, including naturally the space of nonempty compact subsets. "Mutational and Morphological Analysis" offers a structure that embraces and integrates the various approaches, including shape optimization and mathematical morphology. Scientists and graduate students will find here other powerful mathematical tools for studying problems dealing with shapes and images arising in so many fields
Exercices d'analyse non linéaire by
Jean Pierre Aubin(
Book
)
11 editions published in 1987 in French and Italian and held by 122 WorldCat member libraries worldwide
11 editions published in 1987 in French and Italian and held by 122 WorldCat member libraries worldwide
Initiation à l'analyse appliquée by
Jean Pierre Aubin(
Book
)
7 editions published in 1994 in French and held by 111 WorldCat member libraries worldwide
7 editions published in 1994 in French and held by 111 WorldCat member libraries worldwide
Time and money : how long and how much money is needed to regulate a viable economy by
Jean Pierre Aubin(
Book
)
13 editions published between 2013 and 2014 in English and held by 84 WorldCat member libraries worldwide
Presents an unconventional approach to an important topic in economic theory. The author is an expert in the field of viability theory which was motivated by economics at the end of the 1970's. It is used here to analyze how an economy should be dynamically endowed so that it is economically viable. Economic viability requires an assumption on the joint evolution of commodities transactions, fluctuations of prices and numeraire units: the sum of the "transactions values" and the "impact of price fluctuations" should be negative or equal to zero. The book presents a computation of the minimum endowment which restores economic viability and derives the dynamic laws that regulate both transactions and price fluctuations. The target audience primarily comprises openminded and mathematically interested economists but the book may also be beneficial for graduate students
13 editions published between 2013 and 2014 in English and held by 84 WorldCat member libraries worldwide
Presents an unconventional approach to an important topic in economic theory. The author is an expert in the field of viability theory which was motivated by economics at the end of the 1970's. It is used here to analyze how an economy should be dynamically endowed so that it is economically viable. Economic viability requires an assumption on the joint evolution of commodities transactions, fluctuations of prices and numeraire units: the sum of the "transactions values" and the "impact of price fluctuations" should be negative or equal to zero. The book presents a computation of the minimum endowment which restores economic viability and derives the dynamic laws that regulate both transactions and price fluctuations. The target audience primarily comprises openminded and mathematically interested economists but the book may also be beneficial for graduate students
Analyse fonctionnelle appliquee by
Jean Pierre Aubin(
Book
)
6 editions published between 1979 and 1987 in French and held by 59 WorldCat member libraries worldwide
6 editions published between 1979 and 1987 in French and held by 59 WorldCat member libraries worldwide
Tychastic measure of viability risk by
Jean Pierre Aubin(
Book
)
9 editions published between 2014 and 2016 in English and held by 17 WorldCat member libraries worldwide
This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand, and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term ztychastic viability measure of risky is an evolutionary alternative to statistical measures, when dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners
9 editions published between 2014 and 2016 in English and held by 17 WorldCat member libraries worldwide
This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand, and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term ztychastic viability measure of risky is an evolutionary alternative to statistical measures, when dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners
Setvalued analysis by
Jean Pierre Aubin(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the nearimpossible{u2014}it has made a subject which is generally inhospitable to nonspecialists because of its {u2018}family jargon{u2019} appear nonintimidating even to a beginning graduate student." {u2014}The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/setvalued analysis. It includes{u2026}results with many historical comments giving the reader a sound perspective to look at the subject{u2026}The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of setvalued analysis." {u2014}Mathematical Reviews "I recommend this book as one to dig into with considerable pleasure when one already knows the subject ... 'SetValued Analysis{u2019} goes a long way toward providing a much needed basic resource on the subject." {u2014}Bulletin of the American Mathematical Society "This book provides a thorough introduction to multivalued or setvalued analysis ... Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and setvalued maps{u2026}The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work ... Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to setvalued analysis." {u2014}Zentralblatt Math
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the nearimpossible{u2014}it has made a subject which is generally inhospitable to nonspecialists because of its {u2018}family jargon{u2019} appear nonintimidating even to a beginning graduate student." {u2014}The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/setvalued analysis. It includes{u2026}results with many historical comments giving the reader a sound perspective to look at the subject{u2026}The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of setvalued analysis." {u2014}Mathematical Reviews "I recommend this book as one to dig into with considerable pleasure when one already knows the subject ... 'SetValued Analysis{u2019} goes a long way toward providing a much needed basic resource on the subject." {u2014}Bulletin of the American Mathematical Society "This book provides a thorough introduction to multivalued or setvalued analysis ... Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and setvalued maps{u2026}The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work ... Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to setvalued analysis." {u2014}Zentralblatt Math
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Related Identities
 Ekeland, I. (Ivar) 1944 Editor
 Cellina, Arrigo 1941
 Bensoussan, Alain Editor
 Charles, AnneMarie Other Contributor
 Frankowska, Hélène
 Dordan, Olivier Author
 Chen, Luxi
 Nepomiastchy, Pierre Other Contributor
 Vinter, R. B. (Richard B.) Editor
 C.E.R.E.M.A.D.E. Publisher
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Associated Subjects
Approximation theory Artificial intelligence Artificial intelligenceMathematics Biomathematics Boundary value problems Control theory Convex domains Convex functions Decision making Differential equations, Elliptic Differential inclusions Distribution (Probability theory) Economics Economics, Mathematical EconomicsMathematical models Equilibrium (Economics)Mathematical models Feedback control systems Finance FinanceMathematical models Finite element method Functional analysis Game theory Global analysis (Mathematics) Hamiltonian systems Hilbert space Logic, Symbolic and mathematical Macroeconomics MacroeconomicsComputer programs Mathematical analysis Mathematical optimization Mathematical physics Mathematics Metric spaces Neural networks (Computer science) Nonlinear functional analysis Probabilities Resource allocationMathematical models Risk assessment Risk assessmentMathematical models Setvalued maps Shape theory (Topology) Statics and dynamics (Social sciences)Mathematical models System analysis Topology UncertaintyMathematical models
Alternative Names
Aubin, J.
Aubin, J.P.
Aubin, J.P. 1939
Aubin, J. P. (Jean Pierre)
Aubin, Jean P.
Aubin, Jean P. 1939
Aubin, JeanPierre
Aubin, Jean Pierre 1939
JeanPierre Aubin Frans wiskundige
JeanPierre Aubin fransk matematikar
JeanPierre Aubin fransk matematiker
JeanPierre Aubin französischer Mathematiker
JeanPierre Aubin French mathematician
Oben, Ž.P.
Oben, ŽanP'er.
Oben, ŽanP'jer 1939
Обен, Ж.П.
Обэн, Ж.П..
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