Summary
In this chapter, we introduced the concepts of mathematical modeling via the important areas it is largely implemented in or applied to, such as optimization, signal processing, control systems, and control engineering. Mathematical modeling or mathematical programming is the art of transforming a problem into a clear mathematical formulation. Its subsequent algorithmic implementation generates actionable insights and helps build further knowledge about the domain.
The chapter helped us learn the formulation of a mathematical optimization problem in order to arrive at an optimal solution, the formulation being dependent on the domain we intend to investigate. A mathematical optimization model is like a digital twin of a real-world business scenario. It mirrors the business landscape in a strictly mathematical and programming setup, and such an environment becomes particularly relevant for the interpretability of business processes to support high-stake decisions.
In the next chapter, we will find out how mathematical models emphasize the importance of both data and domain knowledge. Additionally, we will learn how ML models can be cast as optimization problems.
