How to optimize more efficiently by two parameters?

Question

Mathematics

Suppose we have a device consisting of two black boxes. Each of the boxes has its own parameter, such as efficiency, by which the performance is evaluated. Suppose that box 1 has an efficiency of n1 = 0.35, and box 2 has an efficiency of n2 = 0.85, then to increase the efficiency of the entire device by n2/n1 times, it is more efficient to increase the efficiency of box 1. That is, increasing the efficiency of n1 by one percent is n2/n1 times more efficient increasing the efficiency n2. Actually, I would like to know who and how studied such properties of multiplication in more detail and how it is used? Any scientific articles, your experience and thoughts are welcome.

Answer 1

I think you are describing the gradient descent method