Decomposition Techniques in Mathematical Programming

Decomposition Techniques in Mathematical Programming
Author: Antonio J. Conejo
Publisher: Springer Science & Business Media
Total Pages: 542
Release: 2006-04-28
Genre: Technology & Engineering
ISBN: 3540276866

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.

Stochastic Decomposition

Stochastic Decomposition
Author: Julia L. Higle
Publisher: Springer Science & Business Media
Total Pages: 237
Release: 2013-11-27
Genre: Mathematics
ISBN: 1461541158

Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.

Building and Solving Mathematical Programming Models in Engineering and Science

Building and Solving Mathematical Programming Models in Engineering and Science
Author: Enrique Castillo
Publisher: John Wiley & Sons
Total Pages: 568
Release: 2011-10-24
Genre: Mathematics
ISBN: 0471461652

Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes: * Discussion and implementation of the GAMS programming system * Unique coverage of compatibility * Illustrative examples that showcase the connection between model and reality * Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises * Real-world applications to probability and statistics, electrical engineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.

Domain Decomposition Methods - Algorithms and Theory

Domain Decomposition Methods - Algorithms and Theory
Author: Andrea Toselli
Publisher: Springer Science & Business Media
Total Pages: 454
Release: 2006-06-20
Genre: Mathematics
ISBN: 3540266623

This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.

Nondifferentiable and Two-Level Mathematical Programming

Nondifferentiable and Two-Level Mathematical Programming
Author: Kiyotaka Shimizu
Publisher: Springer Science & Business Media
Total Pages: 482
Release: 2012-12-06
Genre: Business & Economics
ISBN: 1461563054

The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.

An Introduction to Domain Decomposition Methods

An Introduction to Domain Decomposition Methods
Author: Victorita Dolean
Publisher: SIAM
Total Pages: 242
Release: 2015-12-08
Genre: Science
ISBN: 1611974054

The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?

Cybernetics Approaches in Intelligent Systems

Cybernetics Approaches in Intelligent Systems
Author: Radek Silhavy
Publisher: Springer
Total Pages: 405
Release: 2017-09-04
Genre: Technology & Engineering
ISBN: 3319676180

This book discusses new approaches and methods in the cybernetics, algorithms and software engineering in the scope of the intelligent systems. It brings new approaches and methods to real-world problems and exploratory research that describes novel approaches in the cybernetics, algorithms and software engineering in the scope of the intelligent systems. This book constitutes the refereed proceedings of the Computational Methods in Systems and Software 2017, a conference that provided an international forum for the discussion of the latest high-quality research results in all areas related to computational methods, statistics, cybernetics and software engineering.

50 Years of Integer Programming 1958-2008

50 Years of Integer Programming 1958-2008
Author: Michael Jünger
Publisher: Springer Science & Business Media
Total Pages: 803
Release: 2009-11-06
Genre: Mathematics
ISBN: 3540682791

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.

Optimization Theory for Large Systems

Optimization Theory for Large Systems
Author: Leon S. Lasdon
Publisher: Courier Corporation
Total Pages: 566
Release: 2002-01-01
Genre: Mathematics
ISBN: 9780486419992

Important text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.

Power System Operations

Power System Operations
Author: Antonio J. Conejo
Publisher: Springer
Total Pages: 303
Release: 2017-12-05
Genre: Technology & Engineering
ISBN: 3319694073

This textbook provides a detailed description of operation problems in power systems, including power system modeling, power system steady-state operations, power system state estimation, and electricity markets. The book provides an appropriate blend of theoretical background and practical applications, which are developed as working algorithms, coded in Octave (or Matlab) and GAMS environments. This feature strengthens the usefulness of the book for both students and practitioners. Students will gain an insightful understanding of current power system operation problems in engineering, including: (i) the formulation of decision-making models, (ii) the familiarization with efficient solution algorithms for such models, and (iii) insights into these problems through the detailed analysis of numerous illustrative examples. The authors use a modern, “building-block” approach to solving complex problems, making the topic accessible to students with limited background in power systems. Solved examples are used to introduce new concepts and each chapter ends with a set of exercises.