Decomposition techniques in mathematical programming: engineering and science applications

Abstract

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.The book is organized in five parts.Part I, which includes Chapter 1, provides motivating examples and illustrates how optimization problems with decomposable structure are ubiquitous.Part II describes decomposition theory, algorithms, and procedures.Particularly, Chapter 2 and 3 address solution procedures for linear programming problems with complicating constraints and complicating variables, respectively.Chapter 4 reviews and summarizes