Deterministic Global Optimization

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
Page : 741 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475749496

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Deterministic Global Optimization by Christodoulos A. Floudas Pdf

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.

Author : Reiner Horst,Hoang Tuy
Publisher : Springer Science & Business Media
Page : 705 pages
File Size : 45,8 Mb
Release : 2013-11-27
Category : Business & Economics
ISBN : 9783662025987

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Global Optimization by Reiner Horst,Hoang Tuy Pdf

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.

Author : Yaroslav D. Sergeyev,Dmitri E. Kvasov
Publisher : Springer
Page : 136 pages
File Size : 43,5 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.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 46,5 Mb
Release : 1990-09-15
Category : Business & Economics
ISBN : 3540530320

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A Collection of Test Problems for Constrained Global Optimization Algorithms by Christodoulos A. Floudas,Panos M. Pardalos Pdf

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.

Author : Daniel Scholz
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 49,7 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.

Author : Panos M. Pardalos,Anatoly Zhigljavsky,Julius Žilinskas
Publisher : Springer
Page : 296 pages
File Size : 40,5 Mb
Release : 2016-11-04
Category : Mathematics
ISBN : 9783319299754

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Advances in Stochastic and Deterministic Global Optimization by Panos M. Pardalos,Anatoly Zhigljavsky,Julius Žilinskas Pdf

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Žilinskas who is a leading world expert in global optimization. Professor Žilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and multiple objectives, and application of algorithms for solving real-world practical problems.

Author : Reiner Horst,Hoang Tuy
Publisher : Springer
Page : 0 pages
File Size : 46,7 Mb
Release : 1993
Category : Business & Economics
ISBN : 3662029472

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Global Optimization by Reiner Horst,Hoang Tuy Pdf

The main contents and character of the monograph did not change with respect to the first edition. However, within most chapters we incorporated quite a number of modifications which take into account the recent development of the field, the very valuable suggestions and comments that we received from numerous colleagues and students as well as our own experience while using the book. Some errors and misprints in the first edition are also corrected. May 1992 Reiner Horst Hoang Tuy PREFACE TO THE FIRST EDITION 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.

Author : Reiner Horst,Tuy Hoang
Publisher : Unknown
Page : 728 pages
File Size : 40,8 Mb
Release : 1993
Category : Mathematics
ISBN : STANFORD:36105004417734

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Global Optimization by Reiner Horst,Tuy Hoang Pdf

Author : R. Horst,Panos M. Pardalos,Nguyen Van Thoai
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 45,9 Mb
Release : 2000-12-31
Category : Computers
ISBN : 0792367561

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Introduction to Global Optimization by R. Horst,Panos M. Pardalos,Nguyen Van Thoai Pdf

A textbook for an undergraduate course in mathematical programming for students with a knowledge of elementary real analysis, linear algebra, and classical linear programming (simple techniques). Focuses on the computation and characterization of global optima of nonlinear functions, rather than the locally optimal solutions addressed by most books on optimization. Incorporates the theoretical, algorithmic, and computational advances of the past three decades that help solve globally multi-extreme problems in the mathematical modeling of real world systems. Annotation copyright by Book News, Inc., Portland, OR

Author : Hoang Tuy
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 55,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475728095

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Convex Analysis and Global Optimization by Hoang Tuy Pdf

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.

Author : Yaroslav D. Sergeyev,Roman G. Strongin,Daniela Lera
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 44,5 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781461480426

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Introduction to Global Optimization Exploiting Space-Filling Curves by Yaroslav D. Sergeyev,Roman G. Strongin,Daniela Lera Pdf

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 . ​

Author : Remigijus Paulavičius,Julius Žilinskas
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 52,8 Mb
Release : 2013-10-09
Category : Business & Economics
ISBN : 9781461490937

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Simplicial Global Optimization by Remigijus Paulavičius,Julius Žilinskas Pdf

Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text. Applications benefiting from simplicial partitioning are examined in detail such as nonlinear least squares regression and pile placement optimization in grillage-type foundations. Researchers and engineers will benefit from simplicial partitioning algorithms such as Lipschitz branch and bound, Lipschitz optimization without the Lipschitz constant, heuristic partitioning presented. This book will leave readers inspired to develop simplicial versions of other algorithms for global optimization and even use other non-rectangular partitions for special applications.

Author : Ignacio E. Grossmann
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 40,9 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9781475753318

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Global Optimization in Engineering Design by Ignacio E. Grossmann Pdf

Mathematical Programming has been of significant interest and relevance in engineering, an area that is very rich in challenging optimization problems. In particular, many design and operational problems give rise to nonlinear and mixed-integer nonlinear optimization problems whose modeling and solu tion is often nontrivial. Furthermore, with the increased computational power and development of advanced analysis (e. g. , process simulators, finite element packages) and modeling systems (e. g. , GAMS, AMPL, SPEEDUP, ASCEND, gPROMS), the size and complexity of engineering optimization models is rapidly increasing. While the application of efficient local solvers (nonlinear program ming algorithms) has become widespread, a major limitation is that there is often no guarantee that the solutions that are generated correspond to global optima. In some cases finding a local solution might be adequate, but in others it might mean incurring a significant cost penalty, or even worse, getting an incorrect solution to a physical problem. Thus, the need for finding global optima in engineering is a very real one. It is the purpose of this monograph to present recent developments of tech niques and applications of deterministic approaches to global optimization in engineering. The present monograph is heavily represented by chemical engi neers; and to a large extent this is no accident. The reason is that mathematical programming is an active and vibrant area of research in chemical engineering. This trend has existed for about 15 years.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 50,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302513

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Frontiers in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti mization", "State-of-the-Art in Global Optimization", and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.

Author : David J. Rader
Publisher : John Wiley & Sons
Page : 631 pages
File Size : 48,7 Mb
Release : 2013-06-07
Category : Mathematics
ISBN : 9781118627358

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Deterministic Operations Research by David J. Rader Pdf

Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development. Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas’ Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms. Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the “story” of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book’s various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with MapleTM and MATLAB® content for the discussed calculations. Thoroughly class-tested to ensure a straightforward, hands-on approach, Deterministic Operations Research is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.