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Generalized Benders Decomposition
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Book Synopsis Generalized Benders' Decomposition for Geometric Programming with Several Discrete Variables by : Jae Chul Choi
Download or read book Generalized Benders' Decomposition for Geometric Programming with Several Discrete Variables written by Jae Chul Choi and published by . This book was released on 1987 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Extension of Generalized Benders Decomposition with Applications in Multiple Criteria Optimization by : Christopher James Zappe
Download or read book An Extension of Generalized Benders Decomposition with Applications in Multiple Criteria Optimization written by Christopher James Zappe and published by . This book was released on 1988 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems by : Jean-Charles Régin
Download or read book Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems written by Jean-Charles Régin and published by Springer Science & Business Media. This book was released on 2004-04-07 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2004, held in Nice, France in April 2004. The 23 revised full papers and 7 revised short papers presented together with an invited talk were carefully reviewed and selected from 56 submissions. Methodological and foundational issues from AI, OR, and algorithmics are presented as well as applications to the solution of combinatorial optimization problems in various fields via constraint programming.
Book Synopsis Advanced Optimization for Process Systems Engineering by : Ignacio E. Grossmann
Download or read book Advanced Optimization for Process Systems Engineering written by Ignacio E. Grossmann and published by Cambridge University Press. This book was released on 2021-03-25 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique text covering basic and advanced concepts of optimization theory and methods for process systems engineers. With examples illustrating key concepts and algorithms, and exercises involving theoretical derivations, numerical problems and modeling systems, it is ideal for single-semester, graduate courses in process systems engineering.
Book Synopsis GENERALIZED BENDERS DECOMPOSITION. by : Arthur M. Geoffrion
Download or read book GENERALIZED BENDERS DECOMPOSITION. written by Arthur M. Geoffrion and published by . This book was released on 1970 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: J.F. Benders devised an approach for exploiting the structure of mathematical programming problems with 'complicating variables'. Such problems have the property that temporarily fixing the values of certain variables renders the remaining optimization problem considerably more tractable--perhaps breaking apart into a number of independent smaller problems, or being solvable by a highly efficient known algorithm, or reducing to a convex program in continuous variables whereas the original problem is partly nonconvex or discrete. In this paper, Benders' approach is generalized to a broader class of programs in which the parameterized subproblem need no longer be a linear program. Nonlinear convex duality theory is employed to derive the natural families of 'cuts' corresponding to those in Benders' case. The conditions under which such a generalization is possible are examined in detail from both the theoretical and computational viewpoints. An illustrative specialization is made to the variable factor programming problem introduced by R. Wilson, where it appears to offer an especially attractive approach. (Author).
Book Synopsis Generalized Benders Decomposition by : Kurt O. Jörnsten
Download or read book Generalized Benders Decomposition written by Kurt O. Jörnsten and published by . This book was released on 1980 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Optimization by : Leo Liberti
Download or read book Global Optimization written by Leo Liberti and published by Springer Science & Business Media. This book was released on 2006-02-21 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most global optimization literature focuses on theory. This book, however, contains descriptions of new implementations of general-purpose or problem-specific global optimization algorithms. It discusses existing software packages from which the entire community can learn. The contributors are experts in the discipline of actually getting global optimization to work, and the book provides a source of ideas for people needing to implement global optimization software.
Book Synopsis Disjunctive Programming by : Egon Balas
Download or read book Disjunctive Programming written by Egon Balas and published by Springer. This book was released on 2018-11-27 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Decomposition Techniques in Mathematical Programming by : Antonio J. Conejo
Download or read book Decomposition Techniques in Mathematical Programming written by Antonio J. Conejo and published by Springer Science & Business Media. This book was released on 2006-04-28 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.
Book Synopsis Open Problems in Optimization and Data Analysis by : Panos M. Pardalos
Download or read book Open Problems in Optimization and Data Analysis written by Panos M. Pardalos and published by Springer. This book was released on 2018-12-04 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational and theoretical open problems in optimization, computational geometry, data science, logistics, statistics, supply chain modeling, and data analysis are examined in this book. Each contribution provides the fundamentals needed to fully comprehend the impact of individual problems. Current theoretical, algorithmic, and practical methods used to circumvent each problem are provided to stimulate a new effort towards innovative and efficient solutions. Aimed towards graduate students and researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, this book provides a broad comprehensive approach to understanding the significance of specific challenging or open problems within each discipline. The contributions contained in this book are based on lectures focused on “Challenges and Open Problems in Optimization and Data Science” presented at the Deucalion Summer Institute for Advanced Studies in Optimization, Mathematics, and Data Science in August 2016.
Book Synopsis Computational Improvements to Benders Decomposition for Generalized Fixed Charge Problems by : John Anthony Battilega
Download or read book Computational Improvements to Benders Decomposition for Generalized Fixed Charge Problems written by John Anthony Battilega and published by . This book was released on 1973 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A computationally efficient algorithm has been developed for determining exact or approximate solutions for large scale generalized fixed charge problems. This algorithm is based on a relaxation of the Benders decomposition procedure, combined with a linear mixed integer programming (MIP) algorithm specifically designed to solve the problem associated with Benders decomposition and a computationally improved generalized upper bounding (GUB) algorithm which solves a convex separable programming problem by generalized linear programming. A dynamic partitioning technique is defined and used to improve computational efficiency. All component algorithms have been theoretically and computationally integrated with the relaxed Benders algorithm for maximum efficiency for the generalized fixed charge problem. The research was directed toward the approximate solution of a particular class of large scale generalized fixed charge problems, and extensive computational results for problems of this type are given. As the size of the problem diminishes, the relaxations can be enforced, resulting in a classical Benders decomposition, but with special purpose sub-algorithms and improved convergence properties. Many of the results obtained apply to the sub-algorithms independently of the context in which they were developed. The procedure for solving the associated MIP is applicable to any linear 0/1 problem of Benders form, and the techniques developed for the linear program are applicable to any large scale generalized GUB implementation.
Book Synopsis Global Optimization by : Reiner Horst
Download or read book Global Optimization written by Reiner Horst and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 50 Years of Integer Programming 1958-2008 by : Michael Jünger
Download or read book 50 Years of Integer Programming 1958-2008 written by Michael Jünger and published by Springer Science & Business Media. This book was released on 2009-11-06 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience.
Book Synopsis Cliques, Coloring, and Satisfiability by : David S. Johnson
Download or read book Cliques, Coloring, and Satisfiability written by David S. Johnson and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of a DIMACS Challenge is to encourage and coordinate research in the experimental analysis of algorithms. The First DIMACS Challenge encouraged experimental work in the area of network flow and matchings. This Second DIMACS Challenge, on which this volume is based, took place in conjunction with the DIMACS Special Year on Combinatorial Optimization. Addressed here are three difficult combinatorial optimization problems: finding cliques in a graph, colouring the vertices of a graph, and solving instances of the satisfiability problem. These problems were chosen both for their practical interest and because of their theoretical intractability.
Book Synopsis A Benders Decomposition Method for the Network Design Problem in a Combined Distribution and Assignment Environment by : Kurt O. Jörnsten
Download or read book A Benders Decomposition Method for the Network Design Problem in a Combined Distribution and Assignment Environment written by Kurt O. Jörnsten and published by . This book was released on 1979 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mixed Integer Nonlinear Programming by : Jon Lee
Download or read book Mixed Integer Nonlinear Programming written by Jon Lee and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming by : Ivo Nowak
Download or read book Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming written by Ivo Nowak and published by Springer Science & Business Media. This book was released on 2005-08-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
