Introduction to Optimization

Abstract

This chapter introduces the fundamentals of optimization, including the mathematical formulation of an optimization problem, convexity and types of optimization problems, single- and multi-objective optimization, and other important aspects of optimization such as robust optimization and dynamic optimization. Robustness optimization over time, a recently proposed concept in handling uncertainty, will also be discussed. Performance indicators for evaluating the quality of solutions and performance of optimization algorithms are described. A number of illustrative and real-world optimization problems are provided as examples in explaining the concepts and definitions.