Nonsmooth Vector Functions And Continuous Optimization
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| Author | : V. Jeyakumar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 277 |
| Release | : 2007-10-23 |
| Genre | : Mathematics |
| ISBN | : 0387737170 |
Download Nonsmooth Vector Functions and Continuous Optimization Book in PDF, Epub and Kindle
Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.
| Author | : Friedrich W. Ahnefeld |
| Publisher | : |
| Total Pages | : 385 |
| Release | : 1990 |
| Genre | : Notfallmedizin |
| ISBN | : 9780387520278 |
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| Author | : Frank H. Clarke |
| Publisher | : SIAM |
| Total Pages | : 94 |
| Release | : 1989-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898712416 |
Download Methods of Dynamic and Nonsmooth Optimization Book in PDF, Epub and Kindle
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. 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.
| Author | : Marko M Makela |
| Publisher | : World Scientific |
| Total Pages | : 268 |
| Release | : 1992-05-07 |
| Genre | : Mathematics |
| ISBN | : 9814522414 |
Download Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control Book in PDF, Epub and Kindle
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 | : F.H. Clarke |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 481 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 1475760191 |
Download Nonsmooth Optimization and Related Topics Book in PDF, Epub and Kindle
This volume contains the edited texts of the lect. nres presented at the International School of Mathematics devoted to Nonsmonth Optimization, held from . June 20 to July I, 1988. The site for the meeting was the "Ettore ~Iajorana" Centre for Sci entific Culture in Erice, Sicily. In the tradition of these meetings the main purpose was to give the state-of-the-art of an important and growing field of mathematics, and to stimulate interactions between finite-dimensional and infinite-dimensional op timization. The School was attended by approximately 80 people from 23 countries; in particular it was possible to have some distinguished lecturers from the SO\·iet Union, whose research institutions are here gratt-fnlly acknowledged. Besides the lectures, several seminars were delivered; a special s·~ssion was devoted to numerical computing aspects. The result was a broad exposure. gi ·. ring a deep knowledge of the present research tendencies in the field. We wish to express our appreciation to all the participants. Special mention 5hould be made of the Ettorc ;. . Iajorana Centre in Erice, which helped provide a stimulating and rewarding experience, and of its staff which was fundamental for the success of the meeting. j\, loreover, WP want to extend uur deep appreci
| Author | : Anurag Jayswal |
| Publisher | : CRC Press |
| Total Pages | : 379 |
| Release | : 2022-09-13 |
| Genre | : Technology & Engineering |
| ISBN | : 1000648931 |
Download Continuous Optimization and Variational Inequalities Book in PDF, Epub and Kindle
The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.
| Author | : Ding-zhu Du |
| Publisher | : World Scientific |
| Total Pages | : 482 |
| Release | : 1995-09-20 |
| Genre | : Mathematics |
| ISBN | : 9814500410 |
Download Recent Advances In Nonsmooth Optimization Book in PDF, Epub and Kindle
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.
| Author | : Adil Bagirov |
| Publisher | : Springer |
| Total Pages | : 377 |
| Release | : 2014-08-12 |
| Genre | : Business & Economics |
| ISBN | : 3319081144 |
Download Introduction to Nonsmooth Optimization Book in PDF, Epub and Kindle
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 | : Giorgio Giorgi |
| Publisher | : Elsevier |
| Total Pages | : 615 |
| Release | : 2004-03-10 |
| Genre | : Mathematics |
| ISBN | : 008053595X |
Download Mathematics of Optimization: Smooth and Nonsmooth Case Book in PDF, Epub and Kindle
The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems. · Self-contained· Clear style and results are either proved or stated precisely with adequate references· The authors have several years experience in this field· Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems· Useful long references list at the end of each chapter
| Author | : Frank H. Clarke |
| Publisher | : SIAM |
| Total Pages | : 317 |
| Release | : 1990-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898712564 |
Download Optimization and Nonsmooth Analysis Book in PDF, Epub and Kindle
Mathematical Reviews said of this book that it was 'destined to become a classical reference.' 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.
