# An Introduction to Nonsmooth Analysis

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- Author : Juan Ferrera
- Publisher : Academic Press
- Release : 26 November 2013
- ISBN : 9780128008256
- Page : 164 pages
- Rating : 4.5/5 from 103 voters

## Download An Introduction to Nonsmooth Analysis in PDF, Epub and Kindle

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

- Author : Juan Ferrera
- Publisher : Academic Press
- Release Date : 2013-11-26
- ISBN : 9780128008256

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 Introduction to Nonlinear Analysis: Theory

- Author : Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou
- Publisher : Springer
- Release Date : 2013-11-24
- ISBN : 1461348145

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

### An Introduction to Nonsmooth Analysis

- Author : Juan Ferrera
- Publisher : Unknown
- Release Date : 2013-11-26
- ISBN : 0128007311

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

### Nonsmooth Optimization

- Author : Marko M Mäkelä,Pekka Neittaanmäki
- Publisher : World Scientific
- Release Date : 1992-05-07
- ISBN : 9789814522410

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

### Nonsmooth Analysis and Control Theory

- Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
- Publisher : Springer Science & Business Media
- Release Date : 2008-01-10
- ISBN : 9780387226255

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

### Introduction to Functional Analysis

- Author : Christian Clason
- Publisher : Springer Nature
- Release Date : 2020-11-30
- ISBN : 9783030527846

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

### An Easy Path to Convex Analysis and Applications

- Author : Boris Mordukhovich,Nguyen Mau
- Publisher : Springer Nature
- Release Date : 2022-05-31
- ISBN : 9783031024061

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

### Optima and Equilibria

- Author : Jean-Pierre Aubin
- Publisher : Springer Science & Business Media
- Release Date : 2013-03-09
- ISBN : 9783662035399

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,

### Introduction to Nonsmooth Optimization

- Author : Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
- Publisher : Springer
- Release Date : 2014-08-22
- ISBN : 3319081136

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

### Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics

- Author : Vladimir F. Demyanov,Georgios E. Stavroulakis,L.N. Polyakova,P. D. Panagiotopoulos
- Publisher : Springer Science & Business Media
- Release Date : 2013-11-21
- ISBN : 9781461541134

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

### Convex Analysis and Nonlinear Optimization

- Author : Jonathan Borwein,Adrian S. Lewis
- Publisher : Springer Science & Business Media
- Release Date : 2010-05-05
- ISBN : 9780387312569

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.

### Handbook of Applied Analysis

- Author : Nikolaos S. Papageorgiou,Sophia Th. Kyritsi-Yiallourou
- Publisher : Springer Science & Business Media
- Release Date : 2009-05-31
- ISBN : 9780387789071

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.

### Introduction to Piecewise Differentiable Equations

- Author : Stefan Scholtes
- Publisher : Springer Science & Business Media
- Release Date : 2012-08-01
- ISBN : 9781461443407

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

### Lectures on Nonsmooth Differential Geometry

- Author : Nicola Gigli,Enrico Pasqualetto
- Publisher : Springer Nature
- Release Date : 2020-02-10
- ISBN : 9783030386139

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

### An Introduction to Nonlinear Analysis: Theory

- Author : Zdzisław Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou
- Publisher : Springer Science & Business Media
- Release Date : 2003
- ISBN : 0306473925

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