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An Introduction to Nonsmooth Analysis

An Introduction to Nonsmooth Analysis
  • Author : Juan Ferrera
  • Publsiher : Academic Press
  • Release : 26 November 2013
  • ISBN : 0128008253
  • Pages : 164 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKAn Introduction to Nonsmooth Analysis

Summary:
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
  • Author : Juan Ferrera
  • Publisher : Academic Press
  • Release : 26 November 2013
GET THIS BOOKAn Introduction to Nonsmooth Analysis

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

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An Introduction to Nonlinear Analysis: Theory

An Introduction to Nonlinear Analysis: Theory
  • Author : Zdzisław Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou
  • Publisher : Springer Science & Business Media
  • Release : 26 June 2022
GET THIS BOOKAn Introduction to Nonlinear Analysis: Theory

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

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An Introduction to Nonlinear Analysis: Theory

An Introduction to Nonlinear Analysis: Theory
  • Author : Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou
  • Publisher : Springer Science & Business Media
  • Release : 01 December 2013
GET THIS BOOKAn Introduction to Nonlinear Analysis: Theory

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

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Nonsmooth Optimization

Nonsmooth Optimization
  • Author : Marko M Mäkelä,Pekka Neittaanmäki
  • Publisher : World Scientific
  • Release : 07 May 1992
GET THIS BOOKNonsmooth Optimization

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

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Introduction to Piecewise Differentiable Equations

Introduction to Piecewise Differentiable Equations
  • Author : Stefan Scholtes
  • Publisher : Springer Science & Business Media
  • Release : 01 August 2012
GET THIS BOOKIntroduction to Piecewise Differentiable Equations

​​​​​​​ 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

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Nonsmooth Analysis and Control Theory

Nonsmooth Analysis and Control Theory
  • Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
  • Publisher : Springer Science & Business Media
  • Release : 10 January 2008
GET THIS BOOKNonsmooth Analysis and Control Theory

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

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An Introduction to Nonsmooth Analysis

An Introduction to Nonsmooth Analysis
  • Author : Juan Ferrera
  • Publisher : Anonim
  • Release : 26 November 2013
GET THIS BOOKAn Introduction to Nonsmooth Analysis

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

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Introduction to Nonsmooth Optimization

Introduction to Nonsmooth Optimization
  • Author : Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
  • Publisher : Springer
  • Release : 12 August 2014
GET THIS BOOKIntroduction to Nonsmooth Optimization

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

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Introduction to Functional Analysis

Introduction to Functional Analysis
  • Author : Christian Clason
  • Publisher : Springer Nature
  • Release : 30 November 2020
GET THIS BOOKIntroduction to Functional Analysis

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

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Functional Analysis, Calculus of Variations and Optimal Control

Functional Analysis, Calculus of Variations and Optimal Control
  • Author : Francis Clarke
  • Publisher : Springer Science & Business Media
  • Release : 06 February 2013
GET THIS BOOKFunctional Analysis, Calculus of Variations and Optimal Control

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

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An Easy Path to Convex Analysis and Applications

An Easy Path to Convex Analysis and Applications
  • Author : Boris S. Mordukhovich,Nguyen Mau Nam
  • Publisher : Morgan & Claypool Publishers
  • Release : 01 December 2013
GET THIS BOOKAn Easy Path to Convex Analysis and Applications

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

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Lectures on Nonsmooth Differential Geometry

Lectures on Nonsmooth Differential Geometry
  • Author : Nicola Gigli,Enrico Pasqualetto
  • Publisher : Springer Nature
  • Release : 10 February 2020
GET THIS BOOKLectures on Nonsmooth Differential Geometry

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

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Optimization and Nonsmooth Analysis

Optimization and Nonsmooth Analysis
  • Author : Frank H. Clarke
  • Publisher : SIAM
  • Release : 01 January 1990
GET THIS BOOKOptimization and Nonsmooth Analysis

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,

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Nonsmooth Analysis

Nonsmooth Analysis
  • Author : Winfried Schirotzek
  • Publisher : Springer Science & Business Media
  • Release : 26 May 2007
GET THIS BOOKNonsmooth Analysis

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

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Convex Analysis and Nonlinear Optimization

Convex Analysis and Nonlinear Optimization
  • Author : Jonathan Borwein,Adrian S. Lewis
  • Publisher : Springer Science & Business Media
  • Release : 05 May 2010
GET THIS BOOKConvex Analysis and Nonlinear Optimization

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.

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