Optimization

From Mathematics

Optimization, in pure mathematics, is the mathematical analysis of a problem with the goal of finding the most efficient solution. This usually involves maximizing or minimizing a cost function.

A common example is finding the dimensions of a rectangle such that the area is maximized for a given perimeter. Using the perimeter equation P = 2l + 2w and the area equation A = lw,

, where P is a constant

This gives a quadratic equation. The precise value of the optimal length l can be found by taking the derivative of the equation and finding the root.

We can infer from this that the optimal rectangle is a square, as 2l = P/2, which requires w to also be P/4, making the length and width equal.