Combinatorial Linear Integer And Nonlinear Optimization Apps

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Combinatorial Linear Integer And Nonlinear Optimization Apps

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Author : J. MacGregor Smith
language : en
Publisher: Springer Nature
Release Date : 2021-10-17

Combinatorial Linear Integer And Nonlinear Optimization Apps written by J. MacGregor Smith and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-17 with Mathematics categories.

This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics. The formulation of optimization problems is founded through concepts and techniques from operations research: Combinatorial Optimization, Linear Programming, and Integer and Nonlinear Programming (COLIN). Computer Science (CS) is also relevant and important given the applications of algorithms and Apps/algorithms (A) in solving optimization problems. Each chapter provides an overview of the main concepts of optimization according to COLINA, providing examples through App Inventor and AMPL software applications. All apps developed through the text are available for download. Additionally, the text includes links to the University of Wisconsin NEOS server, designed to handle more computing-intensive problems in complex optimization. Readers are encouraged to have some background in calculus, linear algebra, and related mathematics.

Nonlinear Combinatorial Optimization

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Author : Ding-Zhu Du
language : en
Publisher: Springer
Release Date : 2019-05-31

Nonlinear Combinatorial Optimization written by Ding-Zhu Du and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Mathematics categories.

Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.

Mixed Integer Nonlinear Programming

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Author : Jon Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-02

Mixed Integer Nonlinear Programming written by Jon Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-02 with Mathematics categories.

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.

Facets Of Combinatorial Optimization

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Author : Michael Jünger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-03

Facets Of Combinatorial Optimization written by Michael Jünger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-03 with Mathematics categories.

Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel’s doctoral descendant tree 1983–2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants. This book starts with a personal tribute to Martin Grötschel by the editors (Part I), a contribution by his very special “predecessor” Manfred Padberg on “Facets and Rank of Integer Polyhedra” (Part II), and the doctoral descendant tree 1983–2012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant. The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimization, super classes of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclic graphs and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering. Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, mean-risk optimization and gas network optimization. Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-integer linear optimization for scheduling and routing of fly-in safari planes. The two closing articles are devoted to computational advances in general mixed integer linear optimization, the first by scientists working in industry, the second by scientists working in academia. These articles reflect the “scientific facets” of Martin Grötschel who has set standards in theory, computation and applications.

Handbook Of Combinatorial Optimization

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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Handbook Of Combinatorial Optimization written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).

Handbook Of Combinatorial Optimization 1

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Author : Dingzhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Handbook Of Combinatorial Optimization 1 written by Dingzhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.

Integer And Combinatorial Optimization

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Author : Laurence A. Wolsey
language : en
Publisher: John Wiley & Sons
Release Date : 1999-07-08

Integer And Combinatorial Optimization written by Laurence A. Wolsey and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-08 with Mathematics categories.

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima "A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews "[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews "This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society "This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.

Nonlinear Assignment Problems

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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Nonlinear Assignment Problems written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.

Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly. The purpose of this book is to provide in a single volume, major algorithmic aspects and applications of NAPs as contributed by leading international experts. The chapters included in this book are concerned with major applications and the latest algorithmic solution approaches for NAPs. Approximation algorithms, polyhedral methods, semidefinite programming approaches and heuristic procedures for NAPs are included, while applications of this problem class in the areas of multiple-target tracking in the context of military surveillance systems, of experimental high energy physics, and of parallel processing are presented. Audience: Researchers and graduate students in the areas of combinatorial optimization, mathematical programming, operations research, physics, and computer science.

Combinatorial And Global Optimization

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Author : Panos M Pardalos
language : en
Publisher: World Scientific
Release Date : 2002-04-05

Combinatorial And Global Optimization written by Panos M Pardalos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.

Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans–Williamson relaxation of the maximum cut problem, and the Du–Hwang solution of the Gilbert–Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece. Contents:A Forest Exterior Point Algorithm for Assignment Problems (H Achatz et al.)Location/Allocation of Queuing Facilities in Continuous Space Using Minsum and Minimax Criteria (J Brimberg et al.)Algorithms for the Consistency Analysis in Scenario Projects (R Feldmann et al.)Solving Quadratic Knapsack Problems by Reformulation and Tabu Search. Single Constraint Case (F Glover et al.)Global Optimization Using Dynamic Search Trajectories (A A Groenwold & J A Snyman)On Pareto Efficiency. A General Constructive Existence Principle (G Isac)Piecewise Linear Network Flow Problems (D Kim & P M Pardalos)Semidefinite Programming Approaches for MAX-2-SAT and MAX-3-SAT: Computational Perspectives (E de Klerk & J P Warners)Heuristic Solutions of Vehicle Routing Problems in Supply Chain Management (Y Marinakis & A Migdalas)A New Finite Cone Covering Algorithm for Concave Minimization (C Meyer & B Jaumard)Frequency Assignment for Very Large, Sparse Networks (R Murphey)GPS Network Design: An Application of the Simulated Annealing Heuristic Technique (H A Saleh & P J Dare)Normal Branch and Bound Algorithms for General Nonconvex Quadratic Programming (H Tuy)and other papers Readership: Researchers in numerical & computational mathematics, optimization, combinatorics & graph theory, networking and materials engineering. Keywords:Combinatorial Optimization;Global Optimization

Concepts Of Combinatorial Optimization

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Author : Vangelis Th. Paschos
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-08

Concepts Of Combinatorial Optimization written by Vangelis Th. Paschos and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-08 with Mathematics categories.

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: - On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.