(1) Introduction to OPTIMIZATION

Understanding the role of first-order and second-order derivatives

What is optimization?

Optimization is a technique used to improve a system (biological, physics, engineering) to its optimal point, which means, operating at the level of less energy consumption or less error rate, therefore optimizing a set of metrics. It means making the system perform as well as possible.

Optimization problems are not a recent concern. Some of the first records on mathematical optimization date back to ancient Greece, having been discussed by Pythagoras, Plato, and Aristotle as a way to optimize everyday life and the functioning of the State.

→ Optimization problems are usually solved by searching for a solution in a space defined by a set of coordinates.

We owe to Rene Descartes the use of the visual description (coordinates systems) of the algebraic equations described by al-Khwarizmi.