This chapter provides an introduction and overview of the activities in the area of Deterministic Global Optimization. Section 1.1 introduces the key issues, definitions, and motivation of the global optimization problems and contrasts them with the local optimization problems. Section 1.2 presents the structure of the three classes of mathematical models that we focus on this book. Section 1.3 presents a number of illustrative examples of important global optimization applications. Section 1.4 discusses the approaches that have been proposed in deterministic global optimization and the classes of problems that are addressed. Section 1.5 presents the basic definitions of complexity theory and discusses the worst case difficulties that one faces with global and local optimization problems based on complexity analysis results. Section 1.6 provides a large number of research areas that cross several disciplines and a number of important applications. Section 1.7 discusses the activities in the area of global optimization that consist of books published, conferences held, and the introduction of a journal and a book series. Section 1.8 presents an overview of the contributions that came from the field of chemical engineering. Finally, section 1.9 presents an outline of the five parts of this book.
KeywordsGlobal Optimization Global Optimization Method Nonconvex Optimization Problem Heat Exchanger Network Global Optimization Approach
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