Basic Concepts Of Global Optimization
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Basic Concepts Of Global Optimization
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Author : Oliver Stein
language : en
Publisher: Springer
Release Date : 2022-12-24
Basic Concepts Of Global Optimization written by Oliver Stein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-24 with Mathematics categories.
This textbook is an introduction to global optimization, which treats mathematical facts stringently on the one hand, but also motivates them in great detail and illustrates them with 80 figures. The book is therefore not only aimed at mathematicians, but also at natural scientists, engineers and economists who want to understand and apply mathematically sound methods in their field. With almost two hundred pages, the book provides enough choices to use it as a basis for differently designed lectures on global optimization. The detailed treatment of the global solvability of optimization problems under application-relevant conditions sets a new accent that enriches the stock of previous textbooks on optimization. Using the theory and algorithms of smooth convex optimization, the book illustrates that the global solution of a class of optimization problems frequently encountered in practice is efficiently possible, while for the more difficult-to-handle non-convex problems it develops in detail the ideas of branch-and-bound methods.
Introduction To Nonlinear And Global Optimization
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Author : Eligius M.T. Hendrix
language : en
Publisher: Springer
Release Date : 2010-04-27
Introduction To Nonlinear And Global Optimization written by Eligius M.T. Hendrix and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-27 with Mathematics categories.
This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the presentation of numerous algorithms, examples, and illustrations, designed to improve the reader’s intuition and develop the analytical skills needed to identify optimization problems, classify the structure of a model, and determine whether a solution fulfills optimality conditions.
Global Optimization
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Author : Reiner Horst
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Global Optimization written by Reiner Horst 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 2013-11-27 with Business & Economics categories.
The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years ago would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro perties. Aside from a coherent view of the field much new material is presented. By definition, a multiextremal global optimization problem seeks at least one global minimizer of a real-valued objective function that possesses different local n minimizers. The feasible set of points in IR is usually determined by a system of inequalities. It is well known that in practically all disciplines where mathematical models are used there are many real-world problems which can be formulated as multi extremal global optimization problems.
Introduction To Global Optimization Exploiting Space Filling Curves
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Author : Yaroslav D. Sergeyev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Introduction To Global Optimization Exploiting Space Filling Curves written by Yaroslav D. Sergeyev 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 2013-08-13 with Mathematics categories.
Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .
New Computer Methods For Global Optimization
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Author : Helmut Ratschek
language : en
Publisher: Horwood Publishing Limited
Release Date : 1988
New Computer Methods For Global Optimization written by Helmut Ratschek and has been published by Horwood Publishing Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Provides the methods and algorithms for solving global optimization problems using interval arithmetic tools. Contains methods for unconstrained optimization, optimization over unbounded domains, and constrained optimization. Provides the necessary tools of interval analysis and covers the basic concepts of nonlinear optimization. Unattractive text--looks to be desktop published. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR
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.
Global Optimization
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Author : Stefan Schäffler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
Global Optimization written by Stefan Schäffler 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 2012-06-26 with Mathematics categories.
This self-contained monograph presents a new stochastic approach to global optimization problems arising in a variety of disciplines including mathematics, operations research, engineering, and economics. The volume deals with constrained and unconstrained problems and puts a special emphasis on large scale problems. It also introduces a new unified concept for unconstrained, constrained, vector, and stochastic global optimization problems. All methods presented are illustrated by various examples. Practical numerical algorithms are given and analyzed in detail. The topics presented include the randomized curve of steepest descent, the randomized curve of dominated points, the semi-implicit Euler method, the penalty approach, and active set strategies. The optimal decoding of block codes in digital communications is worked out as a case study and shows the potential and high practical relevance of this new approach. Global Optimization: A Stochastic Approach is an elegant account of a refined theory, suitable for researchers and graduate students interested in global optimization and its applications.
Global Optimization
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Author : Leo Liberti
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-21
Global Optimization written by Leo Liberti 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 2006-02-21 with Business & Economics categories.
Most global optimization literature focuses on theory. This book, however, contains descriptions of new implementations of general-purpose or problem-specific global optimization algorithms. It discusses existing software packages from which the entire community can learn. The contributors are experts in the discipline of actually getting global optimization to work, and the book provides a source of ideas for people needing to implement global optimization software.
Convex Analysis And Global Optimization
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Author : Hoang Tuy
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-31
Convex Analysis And Global Optimization written by Hoang Tuy 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 1998-01-31 with Business & Economics categories.
Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.
Global Optimization
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Author : Aimo Törn
language : en
Publisher: Springer
Release Date : 1989-02-22
Global Optimization written by Aimo Törn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-02-22 with Mathematics categories.
Global optimization is concerned with finding the global extremum (maximum or minimum) of a mathematically defined function (the objective function) in some region of interest. In many practical problems it is not known whether the objective function is unimodal in this region; in many cases it has proved to be multimodal. Unsophisticated use of local optimization techniques is normally inefficient for solving such problems. Therefore, more sophisticated methods designed for global optimization, i.e. global optimization methods, are important from a practical point of view. Most methods discussed here assume that the extremum is attained in the interior of the region of interest, i.e., that the problem is essentially unconstrained. Some methods address the general constrained problem. What is excluded is the treatment of methods designed for problems with a special structure, such as quadratic programming with negatively quadratic forms. This book is the first broad treatment of global optimization with an extensive bibliography covering research done both in east and west. Different ideas and methods proposed for global optimization are classified, described and discussed. The efficiency of algorithms is compared by using both artificial test problems and some practical problems. The solutions of two practical design problems are demonstrated and several other applications are referenced. The book aims at aiding in the education, at stimulating the research in the field, and at advising practitioners in using global optimization methods for solving practical problems.