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Filling a void in chemical engineering and optimization literature, this book presents the theory and methods for nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis. Other topics include modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. The basics of convex analysis and nonlinear optimization are also covered and the elementary concepts of mixed-integer linear optimization are introduced. All chapters have several illustrations and geometrical interpretations of the material as well as suggested problems. Nonlinear and Mixed-Integer Optimization will prove to be an invaluable source--either as a textbook or a reference--for researchers and graduate students interested in continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics, operations research, industrial management, and systems engineering.
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To my wife, Fotini
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Preface Nonlinear and Mixed-Integer Optimization addresses the problem of optimizing an objective function subject to equality and inequality constraints in the presence of continuous and integer variables. These optimization models have many applications in engineering and applied science problems and this is the primary motivation for the plethora of theoretical and algorithmic developments that we have been experiencing during the last two decades. This book aims at presenting the fundamentals of nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis and chemical engineering. The first chapter introduces the reader to the generic formulations of this class of optimization problems and presents a number of illustrative applications. For the remaining chapters, the book contains the following three main parts: Part 1: Fundamentals of Convex Analysis and Nonlinear Optimization Part 2: Fundamentals of Mixed-Integer Optimization Part 3: Applications in Process Synthesis Part 1, comprised of three chapters, focuses on the fundamentals of convex analysis and nonlinear optimization. Chapter 2 discusses the key elements of convex analysis (i.e., convex sets, convex and concave functions, and generalizations of convex and concave functions), which are very important in the study of nonlinear optimization problems. Chapter 3 presents the first and second order optimality conditions for unconstrained and constrained nonlinear optimization. Chapter 4 introduces the basics of duality theory (i.e., the primal problem, the perturbation function, and the dual problem) and presents the weak and strong duality theorem along with the duality gap. Part 1 outlines the basic notions of nonlinear optimization and prepares the reader for Part 2. Part 2, comprised of two chapters, addresses the fundamentals and algorithms for mixed-integer linear and nonlinear optimization models. Chapter 5 provides the basic ideas in mixed-integer linear optimization, outlines the different methods, and discusses the key elements of branch and bound approaches. Chapter 6 introduces the reader to the theoretical and algorithmic developments in mixed-integer nonlinear optimization. After a brief description of the motivation and the formulation of such models, the reader is introduced to (i) decomposition-based approaches (e.g., Generalized Benders Decomposition, Generalized Gross Decomposition), (ii) linearizationbased methods (e.g., Outer Approximation and its variants with Equality Relaxation and Augmented Penalty, and Generalized Outer Approximation), and (iii) comparison between decomposition- and linearization-based methods.
viii Part 3, consisting of four chapters, deals with