An Introduction to Nonsmooth Analysis Book

An Introduction to Nonsmooth Analysis


  • Author : Juan Ferrera
  • Publisher : Academic Press
  • Release Date : 2013-11-26
  • Genre: Mathematics
  • Pages : 164
  • ISBN 10 : 9780128008256

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An Introduction to Nonsmooth Analysis Excerpt :

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 Nonlinear Analysis  Theory Book

An Introduction to Nonlinear Analysis Theory


  • Author : Zdzislaw Denkowski
  • Publisher : Springer
  • Release Date : 2013-11-24
  • Genre: Mathematics
  • Pages : 689
  • ISBN 10 : 1461348145

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An Introduction to Nonlinear Analysis Theory Excerpt :

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.

An Introduction to Nonsmooth Analysis Book

An Introduction to Nonsmooth Analysis


  • Author : Juan Ferrera
  • Publisher : Unknown
  • Release Date : 2013-11-26
  • Genre: Mathematics
  • Pages : 164
  • ISBN 10 : 0128007311

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An Introduction to Nonsmooth Analysis Excerpt :

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 Book

Nonsmooth Analysis and Control Theory


  • Author : Francis H. Clarke
  • Publisher : Springer Science & Business Media
  • Release Date : 2008-01-10
  • Genre: Mathematics
  • Pages : 278
  • ISBN 10 : 9780387226255

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Nonsmooth Analysis and Control Theory Excerpt :

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.

Nonsmooth Optimization Book

Nonsmooth Optimization


  • Author : Marko M Mäkelä
  • Publisher : World Scientific
  • Release Date : 1992-05-07
  • Genre: Mathematics
  • Pages : 268
  • ISBN 10 : 9789814522410

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Nonsmooth Optimization Excerpt :

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. Contents: Part I: Nonsmooth Analysis:IntroductionConvex AnalysisNonsmooth Differential TheoryNonsmooth GeometryNonsmooth Optimization TheoryPart II: Nonsmooth Optimization:IntroductionA Survey of Bundle MethodsProximal Bundle Method for Nonconvex Constrained OptimizationNumerical ExperimentsPart III: Nonsmooth Optimal Control:IntroductionPreliminariesDistributed Parameter Control Problems Optimal Shape Design Boundary Control for Stefan Type Problems Readership: Applied mathematicians, mathematicians, operations researchers, engineers, economists and mathematical physicists. keywords:Nonsmooth Optimization;Nondifferentiable Programming;Bundle Methods;Convex Analysis;Nonconvexity;Subgradients;Tangent and Normal Cones;Optimal Control;Optimal Shape Design;Continuous Casting

Introduction to Nonsmooth Optimization Book

Introduction to Nonsmooth Optimization


  • Author : Adil Bagirov
  • Publisher : Springer
  • Release Date : 2014-08-12
  • Genre: Business & Economics
  • Pages : 372
  • ISBN 10 : 9783319081144

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Introduction to Nonsmooth Optimization Excerpt :

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.

Introduction to Functional Analysis Book

Introduction to Functional Analysis


  • Author : Christian Clason
  • Publisher : Springer Nature
  • Release Date : 2020-11-30
  • Genre: Mathematics
  • Pages : 170
  • ISBN 10 : 9783030527846

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Introduction to Functional Analysis Excerpt :

Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

An Introduction to Nonlinear Analysis  Theory Book

An Introduction to Nonlinear Analysis Theory


  • Author : Zdzisław Denkowski
  • Publisher : Springer Science & Business Media
  • Release Date : 2003
  • Genre: Applied mathematics
  • Pages : 708
  • ISBN 10 : 0306473925

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An Introduction to Nonlinear Analysis Theory Excerpt :

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.

Convex Analysis and Nonlinear Optimization Book

Convex Analysis and Nonlinear Optimization


  • Author : Jonathan Borwein
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-05-05
  • Genre: Mathematics
  • Pages : 310
  • ISBN 10 : 9780387312569

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Convex Analysis and Nonlinear Optimization Excerpt :

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Optimal Control  Stabilization and Nonsmooth Analysis Book

Optimal Control Stabilization and Nonsmooth Analysis


  • Author : Marcio S. de Queiroz
  • Publisher : Springer Science & Business Media
  • Release Date : 2004-04-20
  • Genre: Technology & Engineering
  • Pages : 380
  • ISBN 10 : 3540213309

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Optimal Control Stabilization and Nonsmooth Analysis Excerpt :

This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools.

Introduction to Piecewise Differentiable Equations Book

Introduction to Piecewise Differentiable Equations


  • Author : Stefan Scholtes
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-08-01
  • Genre: Mathematics
  • Pages : 133
  • ISBN 10 : 9781461443407

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Introduction to Piecewise Differentiable Equations Excerpt :

​​​​​​​ This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.

An Easy Path to Convex Analysis and Applications Book

An Easy Path to Convex Analysis and Applications


  • Author : Boris S. Mordukhovich
  • Publisher : Morgan & Claypool Publishers
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 219
  • ISBN 10 : 9781627052382

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An Easy Path to Convex Analysis and Applications Excerpt :

Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical f

Quasidifferentiability and Nonsmooth Modelling in Mechanics  Engineering and Economics Book

Quasidifferentiability and Nonsmooth Modelling in Mechanics Engineering and Economics


  • Author : Vladimir F. Demyanov
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-11-21
  • Genre: Computers
  • Pages : 349
  • ISBN 10 : 9781461541134

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Quasidifferentiability and Nonsmooth Modelling in Mechanics Engineering and Economics Excerpt :

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics. This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems. Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

Dynamics and Bifurcations of Non Smooth Mechanical Systems Book

Dynamics and Bifurcations of Non Smooth Mechanical Systems


  • Author : Remco I. Leine
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-19
  • Genre: Mathematics
  • Pages : 236
  • ISBN 10 : 9783540443988

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Dynamics and Bifurcations of Non Smooth Mechanical Systems Excerpt :

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Nonsmooth Analysis and Control Theory Book

Nonsmooth Analysis and Control Theory


  • Author : Francis H. Clarke
  • Publisher : Springer Science & Business Media
  • Release Date : 1997-12-19
  • Genre: Mathematics
  • Pages : 288
  • ISBN 10 : 9780387983363

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Nonsmooth Analysis and Control Theory Excerpt :

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.