Nonlinear Discrete Optimization

Author : Shmuel Onn
Publisher : European Mathematical Society
Page : 0 pages
File Size : 42,7 Mb
Release : 2010
Category : Combinatorial optimization
ISBN : 3037190930

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Nonlinear Discrete Optimization by Shmuel Onn Pdf

This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. This monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.

Author : Mohit Tawarmalani,Nikolaos V. Sahinidis
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 55,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735321

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by Mohit Tawarmalani,Nikolaos V. Sahinidis Pdf

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Author : Jesus A. De Loera,Raymond Hemmecke,Matthias K?ppe
Publisher : SIAM
Page : 320 pages
File Size : 52,7 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781611972436

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Algebraic and Geometric Ideas in the Theory of Discrete Optimization by Jesus A. De Loera,Raymond Hemmecke,Matthias K?ppe Pdf

In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.

Author : P. Venkataraman
Publisher : John Wiley & Sons
Page : 546 pages
File Size : 53,7 Mb
Release : 2009-03-23
Category : Technology & Engineering
ISBN : 9780470084885

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Applied Optimization with MATLAB Programming by P. Venkataraman Pdf

Technology/Engineering/Mechanical Provides all the tools needed to begin solving optimization problems using MATLAB® The Second Edition of Applied Optimization with MATLAB® Programming enables readers to harness all the features of MATLAB® to solve optimization problems using a variety of linear and nonlinear design optimization techniques. By breaking down complex mathematical concepts into simple ideas and offering plenty of easy-to-follow examples, this text is an ideal introduction to the field. Examples come from all engineering disciplines as well as science, economics, operations research, and mathematics, helping readers understand how to apply optimization techniques to solve actual problems. This Second Edition has been thoroughly revised, incorporating current optimization techniques as well as the improved MATLAB® tools. Two important new features of the text are: Introduction to the scan and zoom method, providing a simple, effective technique that works for unconstrained, constrained, and global optimization problems New chapter, Hybrid Mathematics: An Application, using examples to illustrate how optimization can develop analytical or explicit solutions to differential systems and data-fitting problems Each chapter ends with a set of problems that give readers an opportunity to put their new skills into practice. Almost all of the numerical techniques covered in the text are supported by MATLAB® code, which readers can download on the text's companion Web site www.wiley.com/go/venkat2e and use to begin solving problems on their own. This text is recommended for upper-level undergraduate and graduate students in all areas of engineering as well as other disciplines that use optimization techniques to solve design problems.

Author : Anonim
Publisher : Elsevier
Page : 450 pages
File Size : 43,6 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080867677

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Discrete Optimization I by Anonim Pdf

Discrete Optimization I

Author : Gautam M. Appa,Leonidas Pitsoulis,H. Paul Williams
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 43,8 Mb
Release : 2006-08-18
Category : Mathematics
ISBN : 9780387329420

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Handbook on Modelling for Discrete Optimization by Gautam M. Appa,Leonidas Pitsoulis,H. Paul Williams Pdf

This book aims to demonstrate and detail the pervasive nature of Discrete Optimization. The handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It is done with an academic treatment outlining the state-of-the-art for researchers across the domains of the Computer Science, Math Programming, Applied Mathematics, Engineering, and Operations Research. The book utilizes the tools of mathematical modeling, optimization, and integer programming to solve a broad range of modern problems.

Author : Dennis Michaels
Publisher : Unknown
Page : 115 pages
File Size : 42,7 Mb
Release : 2007
Category : Electronic
ISBN : 3899596587

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Discrete Optimization Techniques for Nonlinear Mixed-integer Optimization Problems Arising from Chemical Engineering by Dennis Michaels Pdf

Author : David Bergman,Andre A. Cire,Willem-Jan van Hoeve,John Hooker
Publisher : Springer
Page : 254 pages
File Size : 55,7 Mb
Release : 2016-11-01
Category : Computers
ISBN : 9783319428499

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Decision Diagrams for Optimization by David Bergman,Andre A. Cire,Willem-Jan van Hoeve,John Hooker Pdf

This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. "Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]

Author : Amir Beck
Publisher : SIAM
Page : 282 pages
File Size : 51,6 Mb
Release : 2014-10-27
Category : Mathematics
ISBN : 9781611973655

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Introduction to Nonlinear Optimization by Amir Beck Pdf

This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.

Author : Ding-Zhu Du,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 42,7 Mb
Release : 2006-08-18
Category : Business & Economics
ISBN : 9780387238302

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Handbook of Combinatorial Optimization by Ding-Zhu Du,Panos M. Pardalos Pdf

This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.

Author : Jon Lee,Sven Leyffer
Publisher : Springer Science & Business Media
Page : 687 pages
File Size : 55,5 Mb
Release : 2011-12-02
Category : Mathematics
ISBN : 9781461419273

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Mixed Integer Nonlinear Programming by Jon Lee,Sven Leyffer Pdf

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.

Author : Egon Balas
Publisher : Springer
Page : 238 pages
File Size : 50,6 Mb
Release : 2018-11-27
Category : Mathematics
ISBN : 9783030001483

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Disjunctive Programming by Egon Balas Pdf

Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business.

Author : North Atlantic Treaty Organization. Systems Science Panel,IBM Canada
Publisher : Unknown
Page : 580 pages
File Size : 44,7 Mb
Release : 1979
Category : Mathematical optimization
ISBN : 0444853227

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Discrete Optimization by North Atlantic Treaty Organization. Systems Science Panel,IBM Canada Pdf

Author : M. Gössel
Publisher : Springer
Page : 114 pages
File Size : 50,6 Mb
Release : 2006-04-11
Category : Technology & Engineering
ISBN : 9783540395102

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Nonlinear Time-discrete Systems by M. Gössel Pdf

Author : Sergiy Butenko,Panos M. Pardalos,Volodymyr Shylo
Publisher : Springer
Page : 639 pages
File Size : 47,7 Mb
Release : 2018-02-20
Category : Mathematics
ISBN : 9783319686400

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Optimization Methods and Applications by Sergiy Butenko,Panos M. Pardalos,Volodymyr Shylo Pdf

Researchers and practitioners in computer science, optimization, operations research and mathematics will find this book useful as it illustrates optimization models and solution methods in discrete, non-differentiable, stochastic, and nonlinear optimization. Contributions from experts in optimization are showcased in this book showcase a broad range of applications and topics detailed in this volume, including pattern and image recognition, computer vision, robust network design, and process control in nonlinear distributed systems. This book is dedicated to the 80th birthday of Ivan V. Sergienko, who is a member of the National Academy of Sciences (NAS) of Ukraine and the director of the V.M. Glushkov Institute of Cybernetics. His work has had a significant impact on several theoretical and applied aspects of discrete optimization, computational mathematics, systems analysis and mathematical modeling.