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Deterministic global optimization : an introduction to the diagonal approach /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer,
[2017]
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| Colección: | SpringerBriefs in optimization.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Sergeyev, Yaroslav D., |d 1963- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjvYvgJKhvthhDGbvxGjFq | |
| 245 | 1 | 0 | |a Deterministic global optimization : |b an introduction to the diagonal approach / |c Yaroslav D. Sergeyev, Dmitri E. Kvasov. |
| 264 | 1 | |a New York, NY : |b Springer, |c [2017] | |
| 300 | |a 1 online resource : |b illustrations | ||
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| 490 | 1 | |a SpringerBriefs in optimization, |x 2190-8354 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Online resource; title from PDF title page (viewed on June 22, 2017). | |
| 505 | 0 | |a Preface; Contents; 1 Lipschitz Global Optimization; 1.1 Problem Statement; 1.2 Lipschitz Condition and Its Geometric Interpretation; 1.3 Multidimensional Approaches; 2 One-Dimensional Algorithms and Their Acceleration; 2.1 One-Dimensional Lipschitz Global Optimization; 2.2 Geometric LGO Methods for Non-differentiable Functions; 2.3 Geometric LGO Methods for Differentiable Functions with the Lipschitz First Derivatives; 2.4 Acceleration Techniques Embedded in the Univariate Global Optimization; 2.5 Numerical Illustrations; 3 Diagonal Approach and Efficient Diagonal Partitions. | |
| 505 | 8 | |a 3.1 General Diagonal Scheme3.2 Analysis of Traditional Diagonal Partition Schemes; 3.3 Non-redundant Diagonal Partition Strategy; 4 Global Optimization Algorithms Based on the Non-redundant Partitions ; 4.1 Multiple Estimates of the Lipschitz Constant; 4.2 Derivative-Free Diagonal Method MultL; 4.2.1 Theoretical Background of MultL: Lower Bounds; 4.2.2 Theoretical Background of MultL: Finding Non-dominated Hyperintervals; 4.2.3 Description of the MultL Algorithm and its Convergence Analysis; 4.3 One-Point-Based Method MultK for Differentiable Problems. | |
| 505 | 8 | |a 4.3.1 Theoretical Background of MultK: Lower Bounds4.3.2 Theoretical Background of MultK: Non-dominated Hyperintervals; 4.3.3 Description of the MultK Algorithm and its Convergence Analysis; 4.4 Numerical Experiments with the MultL and MultK Methods; 4.5 A Case Study: Fitting a Sum of Dumped Sinusoids to a Series of Observations; 4.5.1 Examples Illustrating the Complexity of the Problem; 4.5.2 Derivatives and Simplifications of the Benchmark Objective Functions; 4.5.3 Numerical Examples and Simulation Study; Appendix References. | |
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 6 | |a Optimisation mathématique. | |
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| 650 | 7 | |a Mathematical theory of computation. |2 bicssc | |
| 650 | 7 | |a Mathematical modelling. |2 bicssc | |
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| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Optimización matemática |2 embne | |
| 650 | 7 | |a Mathematical optimization |2 fast | |
| 700 | 1 | |a Kvasov, Dmitri E., |e author. | |
| 758 | |i has work: |a Deterministic global optimization (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFBymVK8WpxQFPFyXX3XwK |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Sergeyev, Yaroslav D., 1963- |t Deterministic global optimization. |d New York, NY : Springer, [2017] |z 9781493971978 |z 1493971972 |w (OCoLC)985081967 |
| 830 | 0 | |a SpringerBriefs in optimization. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4880091 |z Texto completo |
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