Control Nonsmooth Analysis And Optimization

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Nonsmooth Analysis And Control Theory

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Author : Francis H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-10

Nonsmooth Analysis And Control Theory written by Francis H. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-10 with Mathematics categories.

In the last decades the subject of nonsmooth analysis has grown rapidly due to the recognition that nondifferentiable phenomena are more widespread, and play a more important role, than had been thought. In recent years, it has come to play a role in functional analysis, optimization, optimal design, mechanics and plasticity, differential equations, control theory, and, increasingly, in analysis. This volume presents the essentials of the subject clearly and succinctly, together with some of its applications and a generous supply of interesting exercises. The book begins with an introductory chapter which gives the reader a sampling of what is to come while indicating at an early stage why the subject is of interest. 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, yet powerful body of theory. The last chapter, as its name implies, is a self-contained introduction to thetheory of control of ordinary differential equations. End-of-chapter problems also offer scope for deeper understanding. The authors have incorporated in the text a number of new results which clarify the relationships between the different schools of thought in the subject. Their goal is to make nonsmooth analysis accessible to a wider audience. In this spirit, the book is written so as to be used by anyone who has taken a course in functional analysis.

Nonsmooth Optimization

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Author : Marko M. Mäkelä
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1992-01-01

Nonsmooth Optimization written by Marko M. Mäkelä and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.

Introduces various methods for nonsmooth optimization and applies these methods to solve discretized nonsmooth optimal control problems of systems governed by boundary value problems. Annotation copyrighted by Book News, Inc., Portland, OR

Optimal Control Stabilization And Nonsmooth Analysis

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Author : Marcio S. de Queiroz
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-20

Optimal Control Stabilization And Nonsmooth Analysis written by Marcio S. de Queiroz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-20 with Technology & Engineering categories.

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 Functional Analysis

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Author : Christian Clason
language : en
Publisher: Springer Nature
Release Date : 2020-11-30

Introduction To Functional Analysis written by Christian Clason and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-30 with Mathematics categories.

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.

Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control

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Author : Marko M Makela
language : en
Publisher: World Scientific
Release Date : 1992-05-07

Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-07 with Mathematics categories.

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.

Functional Analysis Calculus Of Variations And Optimal Control

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Author : Francis Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-06

Functional Analysis Calculus Of Variations And Optimal Control written by Francis Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-06 with Mathematics categories.

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 as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Nonsmooth Analysis

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Author : Winfried Schirotzek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-26

Nonsmooth Analysis written by Winfried Schirotzek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.

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.

Nonsmooth Approach To Optimization Problems With Equilibrium Constraints

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Author : Jiri Outrata
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-07-31

Nonsmooth Approach To Optimization Problems With Equilibrium Constraints written by Jiri Outrata and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-31 with Business & Economics categories.

This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method. This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.

Convex Analysis And Nonlinear Optimization

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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-30

Convex Analysis And Nonlinear Optimization written by Jonathan M. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-30 with Mathematics categories.

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.

Introduction To Nonsmooth Optimization

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Author : Adil Bagirov
language : en
Publisher: Springer
Release Date : 2014-08-12

Introduction To Nonsmooth Optimization written by Adil Bagirov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Business & Economics categories.

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.