The idea of optimizing things is deeply rooted in everyday life. Concepts such as increasing the fuel efficiency of internal combustion engine cars or increasing the productivity of a sector of a company are indeed optimization problems. Nonetheless, using algorithms to solve optimization problems demands knowing how to mathematically formulate those problems.
This chapter introduces the reader to the mathematical formulation of optimization problems. Assuming no previous knowledge about optimization, it starts by providing an intuitive understanding of what optimization is. It then shows the mathematical formulation of the problem and discusses main features of optimization, such as the relation between maximization and minimization problems, the existence of constraints, multimodality, multi-objective optimization and conflicting goals.