Nonsmooth Analysis
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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.
Optimization And Nonsmooth Analysis
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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1990-01-01
Optimization And Nonsmooth Analysis written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
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, mathematical physics, and various branches of analysis in this reprint volume.
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.
Nonsmooth Mechanics Of Solids
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Author : Jaroslav Haslinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-03
Nonsmooth Mechanics Of Solids written by Jaroslav Haslinger 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 2007-08-03 with Computers categories.
Mechanics have played an important role in mathematics, from infinitesimal calculus, calculus of variations, partial differential equations and numerical methods (finite elements). Originally, mechanics treated smooth objects. Technological progress has evoked the necessity to model and solve more complicated problems, like unilateral contact and friction, plasticity, delamination and adhesion, advanced materials, etc. The new tools include convex analysis, differential calculus for convex functions, and subgradients of convex functions and extensions for nonconvex problems. Nonsmooth mechanics is a relatively complex field, and requires a good knowledge of mechanics and a good background in some parts of modern mathematics. The present volume of lecture notes follows a very successful advanced school, with the aim to cover as much as possible all these aspects. Therefore the contributions cover mechanical aspects as well as the mathematical and numerical treatment.
Recent Advances In Nonsmooth Optimization
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Author : Dingzhu Du
language : en
Publisher: World Scientific
Release Date : 1995
Recent Advances In Nonsmooth Optimization written by Dingzhu Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.
Nonsmooth Optimization Methods
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Author : F. Giannessi
language : en
Publisher: Taylor & Francis
Release Date : 2024-12-20
Nonsmooth Optimization Methods written by F. Giannessi and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-20 with Mathematics categories.
Nonsmooth Optimization Methods and Applications provides an overview of this branch of mathematics, concentrating on the interaction between the theory and its applications.
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.
Nonsmooth Critical Point Theory And Nonlinear Boundary Value Problems
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Author : Leszek Gasinski
language : en
Publisher: CRC Press
Release Date : 2004-07-27
Nonsmooth Critical Point Theory And Nonlinear Boundary Value Problems written by Leszek Gasinski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-27 with Mathematics categories.
Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.
Methods Of Dynamic And Nonsmooth Optimization
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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1989-01-01
Methods Of Dynamic And Nonsmooth Optimization written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
Presents the elements of a unified approach to optimization based on "nonsmooth analysis," a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development, and this work therefore incorporates more recent results than those presented in 1986. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.
Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04
Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".