Global Optimization Using Interval Analysis

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Global Optimization Using Interval Analysis

Eldon Hansen,G. William Walster
Global Optimization Using Interval Analysis Book PDF

Author : Eldon Hansen,G. William Walster
Publisher : CRC Press
Page : 528 pages
File Size : 52,6 Mb
Release : 2003-12-19
Category : Mathematics
ISBN : 0203026926

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Global Optimization Using Interval Analysis by Eldon Hansen,G. William Walster Pdf

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

Global Optimization Using Interval Analysis

Eldon R. Hansen
Global Optimization Using Interval Analysis Book PDF

Author : Eldon R. Hansen
Publisher : CRC Press
Page : 264 pages
File Size : 49,5 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015029863167

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Global Optimization Using Interval Analysis by Eldon R. Hansen Pdf

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

Global Optimization Using Interval Analysis

Eldon Hansen,G. William Walster
Global Optimization Using Interval Analysis Book PDF

Author : Eldon Hansen,G. William Walster
Publisher : CRC Press
Page : 728 pages
File Size : 44,8 Mb
Release : 2003-12-19
Category : Mathematics
ISBN : 0824740599

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Global Optimization Using Interval Analysis by Eldon Hansen,G. William Walster Pdf

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

Global Optimization Using Interval Analysis

Eldon Hansen,G. William Walster
Global Optimization Using Interval Analysis Book PDF

Author : Eldon Hansen,G. William Walster
Publisher : CRC Press
Page : 728 pages
File Size : 50,5 Mb
Release : 2003-12-19
Category : Mathematics
ISBN : 1135520631

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Global Optimization Using Interval Analysis by Eldon Hansen,G. William Walster Pdf

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

Applications of Interval Computations

R. Baker Kearfott,V. Kreinovich
Applications of Interval Computations Book PDF

Author : R. Baker Kearfott,V. Kreinovich
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 41,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334408

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Applications of Interval Computations by R. Baker Kearfott,V. Kreinovich Pdf

Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli cations of numerical methods with automatic result verification, that were pre sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.

New Computer Methods for Global Optimization

Helmut Ratschek,Jon Rokne
New Computer Methods for Global Optimization Book PDF

Author : Helmut Ratschek,Jon Rokne
Publisher : Horwood Publishing Limited
Page : 248 pages
File Size : 52,9 Mb
Release : 1988
Category : Mathematics
ISBN : STANFORD:36105032459104

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New Computer Methods for Global Optimization by Helmut Ratschek,Jon Rokne Pdf

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

Introduction to Interval Analysis

Ramon E. Moore,R. Baker Kearfott,Michael J. Cloud
Introduction to Interval Analysis Book PDF

Author : Ramon E. Moore,R. Baker Kearfott,Michael J. Cloud
Publisher : SIAM
Page : 223 pages
File Size : 43,6 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898717716

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Introduction to Interval Analysis by Ramon E. Moore,R. Baker Kearfott,Michael J. Cloud Pdf

An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.

Deterministic Global Optimization

Yaroslav D. Sergeyev,Dmitri E. Kvasov
Deterministic Global Optimization Book PDF

Author : Yaroslav D. Sergeyev,Dmitri E. Kvasov
Publisher : Springer
Page : 136 pages
File Size : 49,5 Mb
Release : 2017-06-16
Category : Computers
ISBN : 9781493971992

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Deterministic Global Optimization by Yaroslav D. Sergeyev,Dmitri E. Kvasov Pdf

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.

Advances in Convex Analysis and Global Optimization

Nicolas Hadjisavvas,Panos M. Pardalos
Advances in Convex Analysis and Global Optimization Book PDF

Author : Nicolas Hadjisavvas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 40,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302797

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Advances in Convex Analysis and Global Optimization by Nicolas Hadjisavvas,Panos M. Pardalos Pdf

There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

State of the Art in Global Optimization

Christodoulos A. Floudas,Panos M. Pardalos
State of the Art in Global Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 54,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334378

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State of the Art in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.

Rigorous Global Search: Continuous Problems

R. Baker Kearfott
Rigorous Global Search Continuous Problems Book PDF

Author : R. Baker Kearfott
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724950

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Rigorous Global Search: Continuous Problems by R. Baker Kearfott Pdf

This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.

Deterministic Global Optimization

Daniel Scholz
Deterministic Global Optimization Book PDF

Author : Daniel Scholz
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 52,9 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9781461419518

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Deterministic Global Optimization by Daniel Scholz Pdf

This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also presented. The book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science.

Models and Algorithms for Global Optimization

Aimo Törn,Julius Žilinskas
Models and Algorithms for Global Optimization Book PDF

Author : Aimo Törn,Julius Žilinskas
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 43,8 Mb
Release : 2007-04-08
Category : Mathematics
ISBN : 9780387367217

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Models and Algorithms for Global Optimization by Aimo Törn,Julius Žilinskas Pdf

The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.

Stochastic and Global Optimization

G. Dzemyda,V. Saltenis,A. Žilinskas
Stochastic and Global Optimization Book PDF

Author : G. Dzemyda,V. Saltenis,A. Žilinskas
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 45,5 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9780306476488

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Stochastic and Global Optimization by G. Dzemyda,V. Saltenis,A. Žilinskas Pdf

In the paper we propose a model of tax incentives optimization for inve- ment projects with a help of the mechanism of accelerated depreciation. Unlike the tax holidays which influence on effective income tax rate, accelerated - preciation affects on taxable income. In modern economic practice the state actively use for an attraction of - vestment into the creation of new enterprises such mechanisms as accelerated depreciation and tax holidays. The problem under our consideration is the following. Assume that the state (region) is interested in realization of a certain investment project, for ex- ple, the creation of a new enterprise. In order to attract a potential investor the state decides to use a mechanism of accelerated tax depreciation. The foll- ing question arise. What is a reasonable principle for choosing depreciation rate? From the state’s point of view the future investor’s behavior will be rat- nal. It means that while looking at economic environment the investor choose such a moment for investment which maximizes his expected net present value (NPV) from the given project. For this case both criteria and “investment rule” depend on proposed (by the state) depreciation policy. For the simplicity we will suppose that the purpose of the state for a given project is a maximi- tion of a discounted tax payments into the budget from the enterprise after its creation. Of course, these payments depend on the moment of investor’s entry and, therefore, on the depreciation policy established by the state.

Encyclopedia of Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Encyclopedia of Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 55,7 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".