Is approximation by multidimensional polynomials used when optimizing a function of many variables?

Question

Mathematics

Hello! First of all, polynomials of 2 and 3 degrees are of interest. I didn't find any information.
In most cases, the cost of calculating the objective function is many times greater than the cost of the optimization algorithm. Those optimization algorithms can be greatly complicated. It seems that polynomial approximation of already calculated function values ​​can be useful. You can quickly get into the maximum area. First, the usual optimization algorithm is used, and the approximation is based on the already calculated values. Those additional calculations of the objective function are not needed. In other words, we are trying to get the maximum benefit from the already calculated function values.

Answer 1

Considering that the problem of approximating the objective function by polynomials itself contains the task of minimizing the functional, which includes this very objective function, and which, again, will have to be calculated many billions of times (and about which you think that it is difficult to calculate) - the idea looks at least strange.
Well, you need to understand that after the approximation, you need to store the coefficients of this approximation somewhere. In fact, both the CPU and the GPU have a lot of nonsense to calculate something and little memory to store something.