Combinatorial Optimization

Abstract

Optimization is a fundamental topic in mathematics that deals with finding the best solution to a problem from a set of possible solutions. This chapter provides an overview of mathematical optimization, its main objectives, and the methods used to solve optimization problems. It also introduces basic problems such as the modeling of binary decision trees, the pooling problem, the clique problem, and flow models. It concludes with an outlook on online optimization and learning optimization methods, which represent promising areas of research in the field. Overall, this chapter serves as a useful introduction to mathematical optimization, its basic problems, and their practical applications. The chapter is based on a white paper from Bärmann et al. [2].