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Advances in Combinatorial Optimization

Advances in Combinatorial Optimization Author Moustapha Diaby
ISBN-10 9789814704892
Release 2016-01-28
Pages 220
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' Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering. Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the ''traveling salesman problem'' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the ''vertex coloring problem'' (VCP)). This work also represents a proof of the equality of the complexity classes "P" (polynomial time) and "NP" (nondeterministic polynomial time), and makes a contribution to the theory and application of ''extended formulations'' (EFs). On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general. Contents:IntroductionBasic IP Model Using the TSPBasic LP Model Using the TSPGeneric LP Modeling for COPsNon-Symmetry of the Basic (TSP) ModelNon-Applicability of Extended Formulations TheoryIllustrations for Other NP-Complete COPs Readership: Professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general. Key Features:The book offers a new proof of the equality of the complexity classes "P" and "NP"Although our approach is developed using the framework of the TSP, it has natural analogs for the other problems in the NP-Complete class thus providing a unified framework for modeling many combinatorial optimization problems (COPs)The book makes a contribution to the theory and application of Extended Formulations (EFs) refining the notion of EFs by separating the case in which that notion is degenerate from the case in which the notion of EF is well defined/meaningful. It separates the case in which the addition of redundant constraints and variables (for the purpose of establishing EF relations) matters from the case in which the addition of redundant constraints and variables does not matterKeywords:Linear Programming;Convex Optimization;Combinatorial Optimization;Traveling Salesman Problem;NP-Complete Problems;P versus NP'

Optimization Methods in Finance

Optimization Methods in Finance Author Gerard Cornuejols
ISBN-10 9781139460569
Release 2006-12-21
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Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Applications of Optimization with Xpress MP

Applications of Optimization with Xpress MP Author Christelle Guéret
ISBN-10 0954350308
Release 2002
Pages 349
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Applications of Optimization with Xpress MP has been writing in one form or another for most of life. You can find so many inspiration from Applications of Optimization with Xpress MP also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Applications of Optimization with Xpress MP book for free.

Multilinear Subspace Learning

Multilinear Subspace Learning Author Haiping Lu
ISBN-10 9781439857298
Release 2013-12-11
Pages 296
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Due to advances in sensor, storage, and networking technologies, data is being generated on a daily basis at an ever-increasing pace in a wide range of applications, including cloud computing, mobile Internet, and medical imaging. This large multidimensional data requires more efficient dimensionality reduction schemes than the traditional techniques. Addressing this need, multilinear subspace learning (MSL) reduces the dimensionality of big data directly from its natural multidimensional representation, a tensor. Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data gives a comprehensive introduction to both theoretical and practical aspects of MSL for the dimensionality reduction of multidimensional data based on tensors. It covers the fundamentals, algorithms, and applications of MSL. Emphasizing essential concepts and system-level perspectives, the authors provide a foundation for solving many of today’s most interesting and challenging problems in big multidimensional data processing. They trace the history of MSL, detail recent advances, and explore future developments and emerging applications. The book follows a unifying MSL framework formulation to systematically derive representative MSL algorithms. It describes various applications of the algorithms, along with their pseudocode. Implementation tips help practitioners in further development, evaluation, and application. The book also provides researchers with useful theoretical information on big multidimensional data in machine learning and pattern recognition. MATLAB® source code, data, and other materials are available at

Combinatorial Algebra Syntax and Semantics

Combinatorial Algebra  Syntax and Semantics Author Mark V. Sapir
ISBN-10 9783319080314
Release 2014-10-06
Pages 355
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Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the “Further reading and open problems” sections at the end of Chapters 2 –5. The book can also be used for self-study, engaging those beyond t he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.

The Traveling Salesman Problem and Its Variations

The Traveling Salesman Problem and Its Variations Author G. Gutin
ISBN-10 9781402006647
Release 2002-05-31
Pages 830
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A brilliant treatment of a knotty problem in computing. This volume contains chapters written by reputable researchers and provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, and includes a thorough computational analysis of heuristic and metaheuristic algorithms.

Optimization Concepts and Applications in Engineering

Optimization Concepts and Applications in Engineering Author Ashok D. Belegundu
ISBN-10 9780521878463
Release 2011-03-28
Pages 463
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In this revised and enhanced second edition of Optimization Concepts and Applications in Engineering, the already robust pedagogy has been enhanced with more detailed explanations, an increased number of solved examples and end-of-chapter problems. The source codes are now available free on multiple platforms. It is vitally important to meet or exceed previous quality and reliability standards while at the same time reducing resource consumption. This textbook addresses this critical imperative integrating theory, modeling, the development of numerical methods, and problem solving, thus preparing the student to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multiobjective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate courses and for practising engineers in all engineering disciplines, as well as in applied mathematics.

Linear Programming and Network Flows

Linear Programming and Network Flows Author Mokhtar S. Bazaraa
ISBN-10 9781118211328
Release 2011-09-28
Pages 768
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The authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics. The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the Fourth Edition include: The cycling phenomenon in linear programming and the geometry of cycling Duality relationships with cycling Elaboration on stable factorizations and implementation strategies Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods Line search and dual ascent ideas for the out-of-kilter algorithm Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by Notes and References sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study. Linear Programming and Network Flows, Fourth Edition is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques.

The Traveling Salesman Problem

The Traveling Salesman Problem Author David L. Applegate
ISBN-10 9781400841103
Release 2011-09-19
Pages 608
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This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience. The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.

Like a Splinter in Your Mind

Like a Splinter in Your Mind Author Matt Lawrence
ISBN-10 1405125241
Release 2004-07-16
Pages 232
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Like a Splinter in Your Mind leads readers through the myriad of philosophical themes within the Matrix trilogy, helping them to gain a better understanding of the films and of philosophy itself. Offers a way into philosophy through the Matrix films. Covers thirteen of the biggest philosophical questions in thirteen self-sufficient chapters suitable for course use. Demonstrates how each of these questions is illustrated through the events and characters of the films. Considers whether sentient machines are possible, and whether we should expect them to face the same existentialist issues that we do. Familiarises readers with key issues in metaphysics, epistemology, ethics, philosophy of mind, race and gender, existentialism, Taoism and mysticism. Includes a chapter that explains some of the technical elements of the films and confusing aspects of the plot. Also includes a Matrix glossary, and a cast of characters and their related symbolism.

Advanced Engineering Mathematics

Advanced Engineering Mathematics Author Erwin Kreyszig
ISBN-10 9780470458365
Release 2010-12-08
Pages 1264
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The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations.

Combinatorial Optimization

Combinatorial Optimization Author Christos H. Papadimitriou
ISBN-10 9780486320137
Release 2013-04-26
Pages 528
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This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.

Search Methodologies

Search Methodologies Author Edmund K. Burke
ISBN-10 9780387283562
Release 2006-03-20
Pages 620
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This book is a tutorial survey of the methodologies that are at the confluence of several fields: Computer Science, Mathematics and Operations Research. It provides a carefully structured and integrated treatment of the major technologies in optimization and search methodology. The chapter authors are drawn from across Computer Science and Operations Research and include some of the world’s leading authorities in their field. It can be used as a textbook or a reference book to learn and apply these methodologies to a wide range of today’s problems.

Multicriteria Optimization

Multicriteria Optimization Author Matthias Ehrgott
ISBN-10 9783540213987
Release 2005-05-18
Pages 323
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Decision makers in many areas, from industry to engineering and the social sector, face an increasing need to consider multiple, conflicting objectives in their decision processes. In many cases these real world decision problems can be formulated as multicriteria mathematical optimization models. The solution of such models requires appropriate techniques to compute so called efficient, or Pareto optimal, or compromise solutions that - unlike traditional mathematical programming methods - take the contradictory nature of the criteria into account. This book provides the necessary mathematical foundation of multicriteria optimization to solve nonlinear, linear and combinatorial problems with multiple criteria. Motivational examples illustrate the use of multicriteria optimization in practice. Numerous illustrations and exercises as well as an extensive bibliography are provided. In the new edition a chapter on optimality conditions has been added. The linear programming part has been extended and includes new developments. Moreover, motivational examples are now introducing the majority of chapters.

Introduction to Linear Optimization

Introduction to Linear Optimization Author Dimitris Bertsimas
ISBN-10 1886529191
Release 1997-01-01
Pages 587
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Introduction to Linear Optimization has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Linear Optimization also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Linear Optimization book for free.

An Introduction to Continuous Optimization

An Introduction to Continuous Optimization Author Michael Patriksson
ISBN-10 0486802876
Release 2018-12-19
Pages 544
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This treatment focuses on the analysis and algebra underlying the workings of convexity and duality and necessary/sufficient local/global optimality conditions for unconstrained and constrained optimization problems. 2015 edition.

The Analytics Edge

The Analytics Edge Author Dimitris Bertsimas
ISBN-10 098991089X
Release 2016
Pages 462
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"Provides a unified, insightful, modern, and entertaining treatment of analytics. The book covers the science of using data to build models, improve decisions, and ultimately add value to institutions and individuals"--Back cover.