Deterministic Global Optimization
Deterministic Global Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 741

ISBN-13: 147574949X

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The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications.

Deterministic Global Optimization
Deterministic Global Optimization

Author: Yaroslav D. Sergeyev

Publisher: Springer

Published: 2017-06-16

Total Pages: 143

ISBN-13: 1493971999

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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.

Global Optimization
Global Optimization

Author: Reiner Horst

Publisher:

Published: 1990

Total Pages: 696

ISBN-13: 9783662026007

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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.

Recent Advances in Global Optimization
Recent Advances in Global Optimization

Author: Christodoulos A. Floudas

Publisher: Princeton University Press

Published: 2014-07-14

Total Pages: 644

ISBN-13: 1400862523

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This book will present the papers delivered at the first U.S. conference devoted exclusively to global optimization and will thus provide valuable insights into the significant research on the topic that has been emerging during recent years. Held at Princeton University in May 1991, the conference brought together an interdisciplinary group of the most active developers of algorithms for global optimization in order to focus the attention of the mathematical programming community on the unsolved problems and diverse applications of this field. The main subjects addressed at the conference were advances in deterministic and stochastic methods for global optimization, parallel algorithms for global optimization problems, and applications of global optimization. Although global optimization is primarily a mathematical problem, it is relevant to several other disciplines, including computer science, applied mathematics, physical chemistry, molecular biology, statistics, physics, engineering, operations research, communication theory, and economics. Global optimization problems originate from a wide variety of mathematical models of real-world systems. Some of its applications are allocation and location problems and VLSI and data-base design problems. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems
Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems

Author: Esther Andrés-Pérez

Publisher: Springer

Published: 2018-09-06

Total Pages: 538

ISBN-13: 3319898906

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This book contains thirty-five selected papers presented at the International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2017). This was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Topics treated in the various chapters reflect the state of the art in theoretical and numerical methods and tools for optimization, and engineering design and societal applications. The volume focuses particularly on intelligent systems for multidisciplinary design optimization (mdo) problems based on multi-hybridized software, adjoint-based and one-shot methods, uncertainty quantification and optimization, multidisciplinary design optimization, applications of game theory to industrial optimization problems, applications in structural and civil engineering optimum design and surrogate models based optimization methods in aerodynamic design.

A Collection of Test Problems for Constrained Global Optimization Algorithms
A Collection of Test Problems for Constrained Global Optimization Algorithms

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 1990-09-15

Total Pages: 200

ISBN-13: 9783540530329

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Significant research activity has occurred in the area of global optimization in recent years. Many new theoretical, algorithmic, and computational contributions have resulted. Despite the major importance of test problems for researchers, there has been a lack of representative nonconvex test problems for constrained global optimization algorithms. This book is motivated by the scarcity of global optimization test problems and represents the first systematic collection of test problems for evaluating and testing constrained global optimization algorithms. This collection includes problems arising in a variety of engineering applications, and test problems from published computational reports.

Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences
Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences

Author: António Gaspar-Cunha

Publisher: Springer Nature

Published: 2020-11-23

Total Pages: 435

ISBN-13: 3030574229

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This book presents improved and extended versions of selected papers from EUROGEN 2019, a conference with interest on developing or applying evolutionary and deterministic methods in optimization of design and emphasizing on industrial and societal applications.

Handbook of Global Optimization
Handbook of Global Optimization

Author: Panos M. Pardalos

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 571

ISBN-13: 1475753624

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In 1995 the Handbook of Global Optimization (first volume), edited by R. Horst, and P.M. Pardalos, was published. This second volume of the Handbook of Global Optimization is comprised of chapters dealing with modern approaches to global optimization, including different types of heuristics. Topics covered in the handbook include various metaheuristics, such as simulated annealing, genetic algorithms, neural networks, taboo search, shake-and-bake methods, and deformation methods. In addition, the book contains chapters on new exact stochastic and deterministic approaches to continuous and mixed-integer global optimization, such as stochastic adaptive search, two-phase methods, branch-and-bound methods with new relaxation and branching strategies, algorithms based on local optimization, and dynamical search. Finally, the book contains chapters on experimental analysis of algorithms and software, test problems, and applications.