Nonsmooth Analysis
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Optimization And Nonsmooth Analysis
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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1990-01-01
Optimization And Nonsmooth Analysis written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
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.
Nonsmooth Analysis
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Author : Winfried Schirotzek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-26
Nonsmooth Analysis written by Winfried Schirotzek 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 2007-05-26 with Mathematics categories.
This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.
Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control
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Author : Marko M Makela
language : en
Publisher: World Scientific
Release Date : 1992-05-07
Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-07 with Mathematics categories.
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.
Nonsmooth Analysis And Control Theory
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Author : Francis H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-12-19
Nonsmooth Analysis And Control Theory written by Francis H. Clarke 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 1997-12-19 with Mathematics categories.
A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.
Methods Of Dynamic And Nonsmooth Optimization
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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1989-01-01
Methods Of Dynamic And Nonsmooth Optimization written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
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, and this work therefore incorporates more recent results than those presented in 1986. 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.
Optimal Control Via Nonsmooth Analysis
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Author : Philip Daniel Loewen
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Optimal Control Via Nonsmooth Analysis written by Philip Daniel Loewen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.
Constructive Nonsmooth Analysis And Related Topics
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Author : Vladimir F. Demyanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-12
Constructive Nonsmooth Analysis And Related Topics written by Vladimir F. Demyanov 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 2013-11-12 with Mathematics categories.
This volume contains a collection of papers based on lectures and presentations delivered at the International Conference on Constructive Nonsmooth Analysis (CNSA) held in St. Petersburg (Russia) from June 18-23, 2012. This conference was organized to mark the 50th anniversary of the birth of nonsmooth analysis and nondifferentiable optimization and was dedicated to J.-J. Moreau and the late B.N. Pshenichnyi, A.M. Rubinov, and N.Z. Shor, whose contributions to NSA and NDO remain invaluable. The first four chapters of the book are devoted to the theory of nonsmooth analysis. Chapters 5-8 contain new results in nonsmooth mechanics and calculus of variations. Chapters 9-13 are related to nondifferentiable optimization, and the volume concludes with four chapters containing interesting and important historical chapters, including tributes to three giants of nonsmooth analysis, convexity, and optimization: Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov. The last chapter provides an overview and important snapshots of the 50-year history of convex analysis and optimization.
An Introduction To Nonsmooth Analysis
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Author : Juan Ferrera
language : en
Publisher: Academic Press
Release Date : 2013-11-26
An Introduction To Nonsmooth Analysis written by Juan Ferrera and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail. - Includes different kinds of sub and super differentials as well as generalized gradients - Includes also the main tools of the theory, as Sum and Chain Rules or Mean Value theorems - Content is introduced in an elementary way, developing many examples, allowing the reader to understand a theory which is scattered in many papers and research books
Nonsmooth Analysis And Control Theory
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Author : Francis H. Clarke
language : en
Publisher: Springer
Release Date : 2013-03-17
Nonsmooth Analysis And Control Theory written by Francis H. Clarke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-17 with Mathematics categories.
A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.
Regularity Concepts In Nonsmooth Analysis
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Author : Messaoud Bounkhel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-12
Regularity Concepts In Nonsmooth Analysis written by Messaoud Bounkhel 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 2011-11-12 with Mathematics categories.
The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nonsmooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The third and final section contains six different application, with comments in relation to the existing literature.