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Author: J.E. Rubio
Publisher: CRC Press
ISBN: 9780824792817
Category : Mathematics
Languages : en
Pages : 380
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Book Description
This text presents an up-to-date overview of optimization and control theory, including existence theory, modelling, approximation and numerical methods. It also provides a self-contained treatment of the theory and practice of non-standard analysis and its applications, illustrated with problems and research material based on optimization theory. A complete set of detailed exercises and a thorough bibliography arranged by topic are included.;College or university bookstores may order five or more copies at a special student price, available upon request.
Author: J.E. Rubio
Publisher: CRC Press
ISBN: 9780824792817
Category : Mathematics
Languages : en
Pages : 380
Get Book Here
Book Description
This text presents an up-to-date overview of optimization and control theory, including existence theory, modelling, approximation and numerical methods. It also provides a self-contained treatment of the theory and practice of non-standard analysis and its applications, illustrated with problems and research material based on optimization theory. A complete set of detailed exercises and a thorough bibliography arranged by topic are included.;College or university bookstores may order five or more copies at a special student price, available upon request.
Author: Julio Enrique Rubio
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Frank H. Clarke
Publisher: SIAM
ISBN: 0898712564
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Mathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.
Author: E. I. Gordon
Publisher:
ISBN: 9789401700641
Category :
Languages : en
Pages : 440
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Book Description
Author: E.I. Gordon
Publisher: Springer Science & Business Media
ISBN: 940170063X
Category : Mathematics
Languages : en
Pages : 435
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Book Description
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0
Author: Leif O. Arkeryd
Publisher: Springer Science & Business Media
ISBN: 9780792345862
Category : Mathematics
Languages : en
Pages : 392
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Book Description
1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
Author: Vladislav Ėlievich Li︠a︡nt︠s︡e
Publisher:
ISBN:
Category : Generalized spaces
Languages : en
Pages : 264
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Book Description
In Nonstandard Analysis (briefly NSA) there was solved the old problem of substantiation of differential and integral calculus with application of infinitesimals. (This problem seemed to be unsolvable from the times of Leibniz and Euler.) NSA has changed the face of the whole of Mathematics: it is a new mathematical outlook. It is necessary to emphasise that NSA does not object, does not contradict to the Ordinary Mathematics (briefly OM). NSA extends, supplements OM. (This means that all objects, which exist in OM, exist in NSA, too, and all statements which are true in OM retain to be true in NSA.) NSA often simplifies OM and makes it more transparent. NSA states new mathematical theorems and problems. In fact, NSA is a work of the only scientist, namely A. Robinson (1961). His approach to NSA was constructive. In this book we have chosen an axiomatic approach, due to E. Nelson (1977), which is less difficult to learn and apply. (Our exposition, contrary to that of Nelson, is not always strictly logical. Our aim is only some popularization of NSA, and not its foundations.) The text includes some own results of authors. Good supplements to this book are (D-R], [Die], [Lut], [Dav], [Alb], [Cut].
Author: Nigel J Cutland
Publisher: CRC Press
ISBN: 1000724646
Category : Mathematics
Languages : en
Pages : 278
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Book Description
This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.
Author: Marko M Makela
Publisher: World Scientific
ISBN: 9814522414
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.
Author: Frank H. Clarke
Publisher: SIAM
ISBN: 0898712416
Category : Mathematics
Languages : en
Pages : 94
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Book Description
Presents the elements of a unified approach to optimization based on 'nonsmooth analysis', a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.
