Lectures On Mathematical Theory Of Extremum Problems
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Lectures On Mathematical Theory Of Extremum Problems
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Author : Igor Vladimirovich Girsanov
language : en
Publisher:
Release Date : 1972
Lectures On Mathematical Theory Of Extremum Problems written by Igor Vladimirovich Girsanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Functional analysis categories.
The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it does not contain proofs of the fundamental theorems. ) Girsanov's book fills this gap. It contains a systematic exposition of the general principles underlying the derivation of necessary and sufficient conditions for an extremum, in a wide variety of problems. Numerous applications are given to specific extremal problems. The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.
Lectures On Mathematical Theory Of Extremum Problems
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Author : I. V. Girsanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Mathematical Theory Of Extremum Problems written by I. V. Girsanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it does not contain proofs of the fundamental theorems. ) Girsanov's book fills this gap. It contains a systematic exposition of the general principles underlying the derivation of necessary and sufficient conditions for an extremum, in a wide variety of problems. Numerous applications are given to specific extremal problems. The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.
Lectures On Mathematical Theory Of Extremum Problems
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Author : I. V Girsanov
language : en
Publisher:
Release Date : 1976-03-01
Lectures On Mathematical Theory Of Extremum Problems written by I. V Girsanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-03-01 with categories.
Mathematical Optimization Theory And Operations Research
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Author : Anton Eremeev
language : en
Publisher: Springer Nature
Release Date : 2024-06-17
Mathematical Optimization Theory And Operations Research written by Anton Eremeev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-17 with Mathematics categories.
This book constitutes the refereed proceedings of the 23rd International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2024, held in Omsk, Russia, during June 30 - July 6, 2024. The 30 full papers included in this book were carefully reviewed and selected from 79 submissions. This book also contains two invited talk. They were organized in topical sections as follows: mathematical programming; combinatorial optimization; game theory; and operations research.
Nonlinear Functional Analysis
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Author : Klaus Deimling
language : en
Publisher: Courier Corporation
Release Date : 2013-10-09
Nonlinear Functional Analysis written by Klaus Deimling and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-09 with Mathematics categories.
This text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. 1985 edition.
Handbook Of Applied Analysis
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Author : Nikolaos S. Papageorgiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-31
Handbook Of Applied Analysis written by Nikolaos S. Papageorgiou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-31 with Mathematics categories.
This handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. It details many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features make the volume a valuable tool for every researcher working on nonlinear analysis.
Optimal Control Of Odes And Daes
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Author : Matthias Gerdts
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Optimal Control Of Odes And Daes written by Matthias Gerdts and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations. An emphasis is placed on the interplay between the continuous optimal control problem, which typically is defined and analyzed in a Banach space setting, and discrete optimal control problems, which are obtained by discretization and lead to finite dimensional optimization problems. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics and interest in optimal control. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Examples are provided for illustration purposes.
Viability Invariance And Applications
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Author : Ovidiu Carja
language : en
Publisher: Elsevier
Release Date : 2007-07-18
Viability Invariance And Applications written by Ovidiu Carja and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Mathematics categories.
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. - New concepts for multi-functions as the classical tangent vectors for functions - Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions - Clarifying examples, illustrations and numerous problems, completely and carefully solved - Illustrates the applications from theory into practice - Very clear and elegant style
An Introduction To Nonlinear Analysis Applications
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Author : Zdzislaw Denkowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-31
An Introduction To Nonlinear Analysis Applications written by Zdzislaw Denkowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-31 with Computers categories.
This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.
Stable Parametric Programming
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Author : S. Zlobec
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-31
Stable Parametric Programming written by S. Zlobec and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-31 with Business & Economics categories.
Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as `controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis.