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Decomposition Techniques in Mathematical Programming: Engineering and Science Applications

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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 of the even numbered exercises are included as an appendix.

Optimization plainly dominates the design, planning, operation, and control of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable structure 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 variables, and analyzes linear and nonlinear problems, with and without integer 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 computational examples, which facilitate the learning procedure. For the sake of clarity, 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 researchers in Engineering, Operations Research, and Applied Economics. The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, difficult 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.
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