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 Science & Business Media
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 690
  • ISBN 10 : 9781441991584

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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 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 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

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.

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 Easy Path to Convex Analysis and Applications Book

An Easy Path to Convex Analysis and Applications


  • Author : Boris Mordukhovich
  • Publisher : Springer Nature
  • Release Date : 2022-05-31
  • Genre: Mathematics
  • Pages : 202
  • ISBN 10 : 9783031024061

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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 foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.

Optima and Equilibria Book

Optima and Equilibria


  • Author : Jean-Pierre Aubin
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages : 442
  • ISBN 10 : 9783662035399

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Optima and Equilibria Excerpt :

Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.

An Introduction to Nonlinear Optimization Theory Book

An Introduction to Nonlinear Optimization Theory


  • Author : Marius Durea
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2014-01-01
  • Genre: Mathematics
  • Pages : 328
  • ISBN 10 : 9783110427356

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An Introduction to Nonlinear Optimization Theory Excerpt :

The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.

Introduction to Nonsmooth Optimization Book

Introduction to Nonsmooth Optimization


  • Author : Adil Bagirov
  • Publisher : Springer
  • Release Date : 2014-08-22
  • Genre: Business & Economics
  • Pages : 372
  • ISBN 10 : 3319081136

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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 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.

Handbook of Applied Analysis Book

Handbook of Applied Analysis


  • Author : Nikolaos S. Papageorgiou
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-05-31
  • Genre: Mathematics
  • Pages : 793
  • ISBN 10 : 9780387789071

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Handbook of Applied Analysis Excerpt :

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.

Qualitative Analysis of Nonsmooth Dynamics Book

Qualitative Analysis of Nonsmooth Dynamics


  • Author : Alain Léger
  • Publisher : Elsevier
  • Release Date : 2016-04-26
  • Genre: Technology & Engineering
  • Pages : 222
  • ISBN 10 : 9780081012017

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Qualitative Analysis of Nonsmooth Dynamics Excerpt :

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses. Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems Provides a focus on unilateral contact in presence of Coulomb friction Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

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.