Decomposition Techniques in Mathematical Programming: Engineering and Science Applications

ISBN-13: 9783540276852 / Angielski / Twarda / 2006 / 542 str.

Antonio J. Conejo;Enrique Castillo;Roberto Minguez

Opis

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 availabl

Recenzje

From the reviews:

"A review of a large variety of optimization models where decomposition is used, and to present the available methods in a clear, illustrative, and application-oriented way. ... The large number of examples and exercises with applications from economics and electrical, mechanical, energy, and civil engineering makes the book extremely valuable for people working in these areas who want to get a quick ... and qualified, introduction to relevant decomposition techniques. The large number of exercises makes it attractive as a textbook ... ." (K. Schittkowski, Mathematical Reviews, Issue 2007 e)

"Mathematical programming is one of the main techniques used in theoretical and applied operations research (OR). ... This book is primarily oriented to the students in science and engineering. However, its material and style of presentation also make it suitable for students of business management, OR, and applied economics. ... I think that this book would be valuable in the libraries of all institutions that teach advanced mathematical-programming courses ... ." (A. Zilinskas, Interfaces, Vol. 37 (5), 2007)

Spis treści

Motivation and Introduction.- Motivating Examples: Models with Decomposable Structure.- Decomposition Techniques.- Decomposition in Linear Programming: Complicating Constraints.- Decomposition in Linear Programming: Complicating Variables.- Duality.- Decomposition in Nonlinear Programming.- Decomposition in Mixed-Integer Programming.- Other Decomposition Techniques.- Local Sensitivity Analysis.- Local Sensitivity Analysis.- Applications.- Applications.- Computer Codes.- Some GAMS Implementations.- Solution to Selected Exercises.- Exercise Solutions.

Blurb

This textbook for students and practitioners presents a practical approach to decomposition techniques in optimization. It provides an appropriate blend of theoretical background and practical applications in engineering and science, which makes the book interesting for practitioners, as well as engineering, operations research and applied economics graduate and postgraduate students. "Decomposition Techniques in Mathematical Programming" is based on clarifying, illustrative and computational examples and applications from electrical, mechanical, energy and civil engineering as well as applied mathematics and economics. It addresses decomposition in linear programming, mixed-integer linear programming, nonlinear programming, and mixed-integer nonlinear programming, and provides rigorous decomposition algorithms as well as heuristic ones. Practical applications are developed up to working algorithms that can be readily used. The theoretical background of the book is deep enough to be of interest to applied mathematicians. It includes end of chapter exercises and the solutions to the even numbered exercises are included as an appendix.