An Introduction To Nonsmooth Analysis
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| Author | : Juan Ferrera |
| Publisher | : Academic Press |
| Total Pages | : 165 |
| Release | : 2013-11-26 |
| Genre | : Mathematics |
| ISBN | : 0128008253 |
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
| Author | : Francis H. Clarke |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 288 |
| Release | : 2008-01-10 |
| Genre | : Mathematics |
| ISBN | : 0387226257 |
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.
| Author | : Winfried Schirotzek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 380 |
| Release | : 2007-05-26 |
| Genre | : Mathematics |
| ISBN | : 3540713336 |
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.
| Author | : Marko M Makela |
| Publisher | : World Scientific |
| Total Pages | : 268 |
| Release | : 1992-05-07 |
| Genre | : Mathematics |
| ISBN | : 9814522414 |
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.
| Author | : Christian Clason |
| Publisher | : Springer Nature |
| Total Pages | : 166 |
| Release | : 2020-11-30 |
| Genre | : Mathematics |
| ISBN | : 3030527840 |
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.
| Author | : Adil Bagirov |
| Publisher | : Springer |
| Total Pages | : 377 |
| Release | : 2014-08-12 |
| Genre | : Business & Economics |
| ISBN | : 3319081144 |
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.
| Author | : Fabio Ancona |
| Publisher | : World Scientific |
| Total Pages | : 377 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9812776060 |
The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.
| Author | : Philip Daniel Loewen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 112 |
| Release | : 1993 |
| Genre | : Control theory |
| ISBN | : 9780821869963 |
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.
| Author | : Yoshihiro Kanno |
| Publisher | : CRC Press |
| Total Pages | : 439 |
| Release | : 2011-04-05 |
| Genre | : Business & Economics |
| ISBN | : 1420094246 |
"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all the
| Author | : Nikolaos S. Papageorgiou |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 1003 |
| Release | : 2024-07-01 |
| Genre | : Mathematics |
| ISBN | : 3111288323 |
The second edition covers the 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. The new edition includes some new topics on Banach spaces of functions and measures and nonlinear analysis.
