Bayesian And High Dimensional Global Optimization
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Bayesian And High Dimensional Global Optimization
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Author : Anatoly Zhigljavsky
language : en
Publisher: Springer Nature
Release Date : 2021-03-02
Bayesian And High Dimensional Global Optimization written by Anatoly Zhigljavsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-02 with Mathematics categories.
Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book.
Bayesian And High Dimensional Global Optimization Bi Objective Decisions And Partition Based Methods In Bayesian Global Optimization
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Author : Anatoly Zhigljavsky
language : en
Publisher:
Release Date : 2021
Bayesian And High Dimensional Global Optimization Bi Objective Decisions And Partition Based Methods In Bayesian Global Optimization written by Anatoly Zhigljavsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called 'curse of dimensionality'. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book. .
Bayesian Approach To Global Optimization
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Author : Jonas Mockus
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Bayesian Approach To Global Optimization written by Jonas Mockus 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.
·Et moi ... si j'avait su comment en revcnir. One service mathematics has rendered the je o'y semis point alle.' human race. It has put common sense back Jules Verne where it beloogs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense', able to do something with it. Eric T. BclI O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Stochastic Global Optimization
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Author : Anatoly Zhigljavsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-20
Stochastic Global Optimization written by Anatoly Zhigljavsky 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 2007-11-20 with Mathematics categories.
This book aims to cover major methodological and theoretical developments in the ?eld of stochastic global optimization. This ?eld includes global random search and methods based on probabilistic assumptions about the objective function. We discuss the basic ideas lying behind the main algorithmic schemes, formulate the most essential algorithms and outline the ways of their theor- ical investigation. We try to be mathematically precise and sound but at the same time we do not often delve deep into the mathematical detail, referring instead to the corresponding literature. We often do not consider the most g- eral assumptions, preferring instead simplicity of arguments. For example, we only consider continuous ?nite dimensional optimization despite the fact that some of the methods can easily be modi?ed for discrete or in?nite-dimensional optimization problems. The authors’ interests and the availability of good surveys on particular topics have in uenced the choice of material in the book. For example, there are excellent surveys on simulated annealing (both on theoretical and - plementation aspects of this method) and evolutionary algorithms (including genetic algorithms). We thus devote much less attention to these topics than they merit, concentrating instead on the issues which are not that well d- umented in literature. We also spend more time discussing the most recent ideas which have been proposed in the last few years.
High Dimensional Optimization
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Author : Jack Noonan
language : en
Publisher: Springer Nature
Release Date : 2024-05-31
High Dimensional Optimization written by Jack Noonan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-31 with Mathematics categories.
This book is interdisciplinary and unites several areas of applied probability, statistics, and computational mathematics including computer experiments, optimal experimental design, and global optimization. The bulk of the book is based on several recent papers by the authors but also contains new results. Considering applications, this brief highlights multistart and other methods of global optimizations requiring efficient exploration of the domain of optimization. This book is accessible to a wide range of readers; the prerequisites for reading the book are rather low, and many numerical examples are provided that pictorially illustrate the main ideas, methods, and conclusions. The main purpose of this book is the construction of efficient exploration strategies of high-dimensional sets. In high dimensions, the asymptotic arguments could be practically misleading and hence the emphasis on the non-asymptotic regime. An important link with global optimization stems from the observation that approximate covering is one of the key concepts associated with multistart and other key random search algorithms. In addition to global optimization, important applications of the results are computer experiments and machine learning. It is demonstrated that the asymptotically optimal space-filling designs, such as pure random sampling or low-discrepancy point nets, could be rather inefficient in the non-asymptotic regime and the authors suggest ways of increasing the efficiency of such designs. The range of techniques ranges from experimental design, Monte Carlo, and asymptotic expansions in the central limit theorem to multivariate geometry, theory of lattices, and numerical integration. This book could be useful to a wide circle of readers, especially those specializing in global optimization, numerical analysis, computer experiments, and computational mathematics. As specific recipes for improving set exploration schemes are formulated, the book can also be used by the practitioners interested in applications only.
Kernels For Vector Valued Functions
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Author : Mauricio A. Álvarez
language : en
Publisher: Foundations & Trends
Release Date : 2012
Kernels For Vector Valued Functions written by Mauricio A. Álvarez and has been published by Foundations & Trends this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
This monograph reviews different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and regularization methods.
Global Optimization
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Author : Marco Locatelli
language : en
Publisher: SIAM
Release Date : 2013-10-16
Global Optimization written by Marco Locatelli and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Mathematics categories.
This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.
Bayesian Optimization
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Author : Roman Garnett
language : en
Publisher: Cambridge University Press
Release Date : 2023-02-09
Bayesian Optimization written by Roman Garnett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Computers categories.
A comprehensive introduction to Bayesian optimization that starts from scratch and carefully develops all the key ideas along the way.
Pricai 2022 Trends In Artificial Intelligence
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Author : Sankalp Khanna
language : en
Publisher: Springer Nature
Release Date : 2022-11-03
Pricai 2022 Trends In Artificial Intelligence written by Sankalp Khanna and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-03 with Computers categories.
This three-volume set, LNAI 13629, LNAI 13630, and LNAI 13631 constitutes the thoroughly refereed proceedings of the 19th Pacific Rim Conference on Artificial Intelligence, PRICAI 2022, held in Shangai, China, in November 10–13, 2022. The 91 full papers and 39 short papers presented in these volumes were carefully reviewed and selected from 432 submissions. PRICAI covers a wide range of topics in the areas of social and economic importance for countries in the Pacific Rim: artificial intelligence, machine learning, natural language processing, knowledge representation and reasoning, planning and scheduling, computer vision, distributed artificial intelligence, search methodologies, etc.
Global Optimization Methods In Geophysical Inversion
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Author : Mrinal K. Sen
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-21
Global Optimization Methods In Geophysical Inversion written by Mrinal K. Sen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
An up-to-date overview of global optimization methods used to formulate and interpret geophysical observations, for researchers, graduate students and professionals.