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An Introduction To Nonsmooth Analysis

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An Introduction to Nonsmooth Analysis

An Introduction to Nonsmooth Analysis Book
Author : Juan Ferrera
Publisher : Unknown
Release : 2013-11-26
ISBN : 9780128007310
Language : En, Es, Fr & De

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Book Description :

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

An Introduction to Nonsmooth Analysis

An Introduction to Nonsmooth Analysis Book
Author : Juan Ferrera
Publisher : Academic Press
Release : 2013-11-26
ISBN : 0128008253
Language : En, Es, Fr & De

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Book Description :

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

Nonsmooth Analysis Book
Author : Winfried Schirotzek
Publisher : Springer Science & Business Media
Release : 2007-05-26
ISBN : 3540713336
Language : En, Es, Fr & De

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Book Description :

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.

An Introduction to Nonlinear Analysis Theory

An Introduction to Nonlinear Analysis  Theory Book
Author : Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 1441991581
Language : En, Es, Fr & De

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Book Description :

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors. The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.

Regularity Concepts in Nonsmooth Analysis

Regularity Concepts in Nonsmooth Analysis Book
Author : Messaoud Bounkhel
Publisher : Springer Science & Business Media
Release : 2011-11-12
ISBN : 1461410193
Language : En, Es, Fr & De

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Book Description :

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.

Introduction to Nonsmooth Optimization

Introduction to Nonsmooth Optimization Book
Author : Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
Publisher : Springer
Release : 2014-08-12
ISBN : 3319081144
Language : En, Es, Fr & De

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Book Description :

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

Topological Aspects of Nonsmooth Optimization

Topological Aspects of Nonsmooth Optimization Book
Author : Vladimir Shikhman
Publisher : Springer Science & Business Media
Release : 2011-11-18
ISBN : 1461418976
Language : En, Es, Fr & De

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Book Description :

This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness. Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory. ​ ​

Optimal Control Via Nonsmooth Analysis

Optimal Control Via Nonsmooth Analysis Book
Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Release : 1993
ISBN : 9780821869963
Language : En, Es, Fr & De

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Book Description :

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.

Nonsmooth Optimization

Nonsmooth Optimization Book
Author : Marko M. Mäkelä,Pekka Neittaanmäki
Publisher : World Scientific Publishing Company Incorporated
Release : 1992-01-01
ISBN : 9789810207731
Language : En, Es, Fr & De

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Book Description :

Introduces various methods for nonsmooth optimization and applies these methods to solve discretized nonsmooth optimal control problems of systems governed by boundary value problems. Annotation copyrighted by Book News, Inc., Portland, OR

Optimization and Nonsmooth Analysis

Optimization and Nonsmooth Analysis Book
Author : Frank H. Clarke
Publisher : Society for Industrial and Applied Mathematics
Release : 1987-01-01
ISBN : 9780898712568
Language : En, Es, Fr & De

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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.

Nonsmooth Analysis and Control Theory

Nonsmooth Analysis and Control Theory Book
Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Publisher : Springer Science & Business Media
Release : 1997-12-19
ISBN : 9780387983363
Language : En, Es, Fr & De

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Book Description :

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.

An Introduction to Piecewise Smooth Dynamics

An Introduction to Piecewise Smooth Dynamics Book
Author : Paul Glendinning,Mike R. Jeffrey
Publisher : Springer Nature
Release : 2019-10-21
ISBN : 3030236897
Language : En, Es, Fr & De

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Book Description :

This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided in two complementary courses: piecewise smooth flows and maps, respectively. Starting from well known theoretical results, the authors bring the reader into the latest challenges in the field, going through stability analysis, bifurcation, singularities, decomposition theorems and an introduction to kneading theory. Both courses contain many examples which illustrate the theoretical concepts that are introduced.

Functional Analysis Calculus of Variations and Optimal Control

Functional Analysis  Calculus of Variations and Optimal Control Book
Author : Francis Clarke
Publisher : Springer Science & Business Media
Release : 2013-02-06
ISBN : 1447148207
Language : En, Es, Fr & De

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Book Description :

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Nonsmooth Analysis and Control Theory

Nonsmooth Analysis and Control Theory Book
Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Publisher : Springer Science & Business Media
Release : 2008-01-10
ISBN : 0387226257
Language : En, Es, Fr & De

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Book Description :

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.

Lectures on Nonsmooth Differential Geometry

Lectures on Nonsmooth Differential Geometry Book
Author : Nicola Gigli,Enrico Pasqualetto
Publisher : Springer Nature
Release : 2020-02-10
ISBN : 3030386139
Language : En, Es, Fr & De

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Book Description :

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking a comprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.

Nonsmooth Mechanics and Analysis

Nonsmooth Mechanics and Analysis Book
Author : Pierre Alart,Olivier Maisonneuve,R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
Release : 2005-11-17
ISBN : 9780387291963
Language : En, Es, Fr & De

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Book Description :

This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification. Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics. Audience This book is intended for researchers in mathematics and mechanics.

Applied Nonlinear Functional Analysis

Applied Nonlinear Functional Analysis Book
Author : Nikolaos S. Papageorgiou,Patrick Winkert
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2018-08-06
ISBN : 3110532980
Language : En, Es, Fr & De

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Book Description :

The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.

Optimization and Nonsmooth Analysis

Optimization and Nonsmooth Analysis Book
Author : Frank H. Clarke
Publisher : SIAM
Release : 1990-01-01
ISBN : 9781611971309
Language : En, Es, Fr & De

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Book Description :

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.

Lectures on Variational Analysis

Lectures on Variational Analysis Book
Author : Asen L. Dontchev
Publisher : Springer
Release : 2021-11-05
ISBN : 9783030799106
Language : En, Es, Fr & De

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Book Description :

This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis would be helpful, but all necessary background material is included in the book.

An Introduction to Nonlinear Analysis

An Introduction to Nonlinear Analysis Book
Author : Zdzislaw Denkowski,Stanislaw Migorski,Nikolaos S. Papageorgiou
Publisher : Unknown
Release : 2014-09-01
ISBN : 9781441991591
Language : En, Es, Fr & De

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Book Description :

Download An Introduction to Nonlinear Analysis book written by Zdzislaw Denkowski,Stanislaw Migorski,Nikolaos S. Papageorgiou, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.