Decomposition Techniques in Mathematical Programming

1. Front Matter

   Pages I-XVI

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2. Motivation and Introduction

   1. Front Matter

      Pages 1-1

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   2. Motivating Examples: Models with Decomposable Structure

      Pages 3-64

3. Decomposition Techniques

   1. Front Matter

      Pages 65-65

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   2. Decomposition in Linear Programming: Complicating Constraints

      Pages 67-106

   3. Decomposition in Linear Programming: Complicating Variables

      Pages 107-139

   4. Duality

      Pages 141-185

   5. Decomposition in Nonlinear Programming

      Pages 187-242

   6. Decomposition in Mixed-Integer Programming

      Pages 243-270

   7. Other Decomposition Techniques

      Pages 271-299

4. Local Sensitivity Analysis

   1. Front Matter

      Pages 301-301

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   2. Local Sensitivity Analysis

      Pages 303-346

5. Applications

   1. Front Matter

      Pages 347-347

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   2. Applications

      Pages 349-393

6. Computer Codes

   1. Front Matter

      Pages 395-395

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   2. Some GAMS Implementations

      Pages 397-417

7. Solution to Selected Exercises

   1. Front Matter

      Pages 419-419

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   2. Exercise Solutions

      Pages 421-529

8. Back Matter

   Pages 531-541

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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.

• Decomposition Techniques
• Nonstandard Optimization Methods
• Operations Research
• algorithm
• algorithms
• calculus
• civil engineering
• linear optimization
• mathematical programming
• nonlinear optimization
• optimization
• programming

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. Žilinskas, Interfaces, Vol. 37 (5), 2007)

• E.T.S. Ingenieros Industriales, Universidad de Castilla — La Mancha, Ciudad Real, Spain

  Antonio J. Conejo, Raquel García-Bertrand

• Escuela de Ingenieros de Caminos, Universidad de Cantabria, Santander, Spain

  Enrique Castillo

• E.T.S. Ingenieros de Caminos, Universidad de Castilla — La Mancha, Ciudad Real, Spain

  Roberto Mínguez

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