Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming
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Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming
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Author : Mohit Tawarmalani
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-10-31
Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming written by Mohit Tawarmalani 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 2002-10-31 with Business & Economics categories.
This book provides an insightful and comprehensive treatment of convexification and global optimization of continuous and mixed-integer nonlinear programs. Developed for students, researchers, and practitioners, the book covers theory, algorithms, software, and applications. This thought-provoking book: -develops a powerful and widely-applicable framework for constructing closed-form expressions of convex envelopes of nonlinear functions; -presents a systematic treatment of branch-and-bound, while providing acceleration mechanisms and enhancements; -unifies ideas at the interface between operations research and computer science, devising efficient algorithmic implementation for global optimization; offers students, modelers, and algorithm developers a rich collection of models, applications, and numerical examples; -elucidates through geometric interpretations the concepts discussed throughout the book; -shows how optimization theory can lead to breakthroughs in diverse application areas, including molecular design, process and product design, facility location, and supply chain design and operation; -demonstrates that the BARON software developed by the authors can solve global optimization problems heretofore considered intractable, in an entirely automated manner on a personal computer. Audience: This book will be of interest to researchers in operations research, management science, applied mathematics, computer science, computational chemistry, and all branches of engineering. In addition, the book can be used in graduate level courses in nonlinear optimization, integer programming, global optimization, convex analysis, applied mathematics, and engineering design.
Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming
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Author : Mohit Tawarmalani
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming written by Mohit Tawarmalani 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 2013-04-17 with Mathematics categories.
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.
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.
Global Optimization And Constraint Satisfaction
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Author : COCOS 200
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-05
Global Optimization And Constraint Satisfaction written by COCOS 200 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 2003-11-05 with Business & Economics categories.
This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Global Constraints Optimization and Costraint Satisfaction, COCOS 2002, held in Valbonne-Sophia Antipolis, France in October 2002. The 15 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address current issues in global optimization, mathematical programming, and constraint programming; they are grouped in topical sections on optimization, constraint satisfaction, and benchmarking.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Integer Programming And Combinatorial Optimization
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Author : Andrea Lodi
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-08
Integer Programming And Combinatorial Optimization written by Andrea Lodi 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 2008-05-08 with Computers categories.
This book constitutes the refereed proceedings of the 13th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2008, held in Bertinoro, Italy, in May 2008. The 32 revised full papers presented were carefully reviewed and selected from 95 submissions. The papers cover various aspects of integer programming and combinatorial optimization and present recent developments in theory, computation, and applications in that area. Topics included are such as approximation algorithms, branch and bound algorithms, branch and cut algorithms, computational biology, computational complexity, computational geometry, cutting plane algorithms, diophantine equations, geometry of numbers, graph and network algorithms, integer programming, matroids and submodular functions, on-line algorithms and competitive analysis, polyhedral combinatorics, randomized algorithms, random graphs, scheduling theory and scheduling algorithms, and semidefinite programs.
Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming
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Author : Ivo Nowak
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-28
Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming written by Ivo Nowak 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 2006-03-28 with Computers categories.
Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: • A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. • In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. • The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.
Frontiers In Global Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Frontiers In Global Optimization written by Christodoulos A. Floudas 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.
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.
Global Optimization And Constraint Satisfaction
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Author : Christophe Jermann
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-24
Global Optimization And Constraint Satisfaction written by Christophe Jermann 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 2005-05-24 with Computers categories.
This book constitutes the throughly refereed post-proceedings of the Second International Workshop on Global Optimization and Constraint Satisfaction, COCOS 2003, held in Lausanne, Switzerland in Nowember 2003. The 13 revised full papers presented were carefully selected and went through two rounds of reviewing and improvement. The papers are devoted to theoretical, algorithmic, and application-oriented issues in global constrained optimization and constraint satisfaction; they are organized in topical sections on constraint satisfaction problems, global optimization, and applications.
Introduction To Global Optimization
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Author : R. Horst
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-06-30
Introduction To Global Optimization written by R. Horst 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 1995-06-30 with Mathematics categories.
Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications. Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved. Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering.