An Introduction To Continuous Optimization
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An Introduction To Continuous Optimization
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Author : Niclas Andreasson
language : en
Publisher: Courier Dover Publications
Release Date : 2020-01-15
An Introduction To Continuous Optimization written by Niclas Andreasson and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Mathematics categories.
This treatment focuses on the analysis and algebra underlying the workings of convexity and duality and necessary/sufficient local/global optimality conditions for unconstrained and constrained optimization problems. 2015 edition.
Introduction To Continuous Optimization
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Author : Roman A. Polyak
language : en
Publisher: Springer Nature
Release Date : 2021-04-29
Introduction To Continuous Optimization written by Roman A. Polyak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-29 with Mathematics categories.
This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization. The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why. The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization. The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described. Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.
An Introduction To Continuous Optimization
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Author : Niclas Andréasson
language : en
Publisher:
Release Date : 2016
An Introduction To Continuous Optimization written by Niclas Andréasson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Anintroduction To Continuous Optimization Second Edition
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Author : Niclas Andreasson
language : en
Publisher: Studentlitteratur AB
Release Date : 2013-10-01
Anintroduction To Continuous Optimization Second Edition written by Niclas Andreasson and has been published by Studentlitteratur AB this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Mathematics categories.
Optimisation, or mathematical programming, is a fundamental subject within decision science and operations research, in which mathematical decision models are constructed, analysed, and solved. The books focus lies on providing a basis for the analysis of optimisation models and of candidate optimal solutions for continuous optimisation models. The main part of the mathematical material therefore concerns the analysis and linear algebra that underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimisation problems. Natural algorithms are then developed from these optimality conditions, and their most important convergence characteristics are analysed. The book answers many more questions of the form Why? and Why not? than How?. We use only elementary mathematics in the development of the book, yet are rigorous throughout. The book provides lecture, exercise and reading material for a first course on continuous optimisation and mathematical programming, geared towards third-year students, and has already been used as such for nearly ten years. The preface to the second edition describes the main changes made since the first, 2005, edition. The book can be used in mathematical optimisation courses at any mathematics, engineering, economics, and business schools. It is a perfect starting book for anyone who wishes to develop his/her understanding of the subject of optimisation, before actually applying it.
Anintroduction To Continuous Optimization Second Edition
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Author : Niclas Andreasson
language : en
Publisher: Studentlitteratur AB
Release Date : 2013-10-01
Anintroduction To Continuous Optimization Second Edition written by Niclas Andreasson and has been published by Studentlitteratur AB this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Mathematics categories.
Optimisation, or mathematical programming, is a fundamental subject within decision science and operations research, in which mathematical decision models are constructed, analysed, and solved. The books focus lies on providing a basis for the analysis of optimisation models and of candidate optimal solutions for continuous optimisation models. The main part of the mathematical material therefore concerns the analysis and linear algebra that underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimisation problems. Natural algorithms are then developed from these optimality conditions, and their most important convergence characteristics are analysed. The book answers many more questions of the form Why? and Why not? than How?. We use only elementary mathematics in the development of the book, yet are rigorous throughout. The book provides lecture, exercise and reading material for a first course on continuous optimisation and mathematical programming, geared towards third-year students, and has already been used as such for nearly ten years. The preface to the second edition describes the main changes made since the first, 2005, edition. The book can be used in mathematical optimisation courses at any mathematics, engineering, economics, and business schools. It is a perfect starting book for anyone who wishes to develop his/her understanding of the subject of optimisation, before actually applying it.
Algorithms For Continuous Optimization
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Author : E. Spedicato
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algorithms For Continuous Optimization written by E. Spedicato 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 2012-12-06 with Mathematics categories.
The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.
A Brief Introduction To Continuous Evolutionary Optimization
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Author : Oliver Kramer
language : en
Publisher: Springer
Release Date : 2013-12-07
A Brief Introduction To Continuous Evolutionary Optimization written by Oliver Kramer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-07 with Computers categories.
Practical optimization problems are often hard to solve, in particular when they are black boxes and no further information about the problem is available except via function evaluations. This work introduces a collection of heuristics and algorithms for black box optimization with evolutionary algorithms in continuous solution spaces. The book gives an introduction to evolution strategies and parameter control. Heuristic extensions are presented that allow optimization in constrained, multimodal and multi-objective solution spaces. An adaptive penalty function is introduced for constrained optimization. Meta-models reduce the number of fitness and constraint function calls in expensive optimization problems. The hybridization of evolution strategies with local search allows fast optimization in solution spaces with many local optima. A selection operator based on reference lines in objective space is introduced to optimize multiple conflictive objectives. Evolutionary search is employed for learning kernel parameters of the Nadaraya-Watson estimator and a swarm-based iterative approach is presented for optimizing latent points in dimensionality reduction problems. Experiments on typical benchmark problems as well as numerous figures and diagrams illustrate the behavior of the introduced concepts and methods.
A Brief Introduction To Continuous Evolutionary Optimization
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Author : Oliver Kramer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-04
A Brief Introduction To Continuous Evolutionary Optimization written by Oliver Kramer 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 2013-12-04 with Technology & Engineering categories.
Practical optimization problems are often hard to solve, in particular when they are black boxes and no further information about the problem is available except via function evaluations. This work introduces a collection of heuristics and algorithms for black box optimization with evolutionary algorithms in continuous solution spaces. The book gives an introduction to evolution strategies and parameter control. Heuristic extensions are presented that allow optimization in constrained, multimodal and multi-objective solution spaces. An adaptive penalty function is introduced for constrained optimization. Meta-models reduce the number of fitness and constraint function calls in expensive optimization problems. The hybridization of evolution strategies with local search allows fast optimization in solution spaces with many local optima. A selection operator based on reference lines in objective space is introduced to optimize multiple conflictive objectives. Evolutionary search is employed for learning kernel parameters of the Nadaraya-Watson estimator and a swarm-based iterative approach is presented for optimizing latent points in dimensionality reduction problems. Experiments on typical benchmark problems as well as numerous figures and diagrams illustrate the behavior of the introduced concepts and methods.
Introduction To The Theory Of Nonlinear Optimization
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Author : Johannes Jahn
language : en
Publisher: Springer Nature
Release Date : 2020-07-02
Introduction To The Theory Of Nonlinear Optimization written by Johannes Jahn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Business & Economics categories.
This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Deterministic Global Optimization
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Author : Yaroslav D. Sergeyev
language : en
Publisher: Springer
Release Date : 2017-06-16
Deterministic Global Optimization written by Yaroslav D. Sergeyev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-16 with Computers categories.
This book begins with a concentrated introduction into deterministic global optimization and moves forward to present new original results from the authors who are well known experts in the field. Multiextremal continuous problems that have an unknown structure with Lipschitz objective functions and functions having the first Lipschitz derivatives defined over hyperintervals are examined. A class of algorithms using several Lipschitz constants is introduced which has its origins in the DIRECT (DIviding RECTangles) method. This new class is based on an efficient strategy that is applied for the search domain partitioning. In addition a survey on derivative free methods and methods using the first derivatives is given for both one-dimensional and multi-dimensional cases. Non-smooth and smooth minorants and acceleration techniques that can speed up several classes of global optimization methods with examples of applications and problems arising in numerical testing of global optimization algorithms are discussed. Theoretical considerations are illustrated through engineering applications. Extensive numerical testing of algorithms described in this book stretches the likelihood of establishing a link between mathematicians and practitioners. The authors conclude by describing applications and a generator of random classes of test functions with known local and global minima that is used in more than 40 countries of the world. This title serves as a starting point for students, researchers, engineers, and other professionals in operations research, management science, computer science, engineering, economics, environmental sciences, industrial and applied mathematics to obtain an overview of deterministic global optimization.