The Arduino is capable to calculate the minimum of a function with 300 variables?

Can you give their name and type please?

I assume you will use a global array of integers for your variables.

int var[300]; // 600 bytes

// for the search range per param

int rangeBegin[300]; // 600 bytes

int rangeEnd[300]; // 600 bytes

In total 1800 bytes. Given the fact that an UNO has only 2K RAM you should at least go for a MEGA.

Then there is the question if the parameters have a linear behavior or polynomal, power or exponential

Think I would go for an heuristic or genetic algorithm, generate random parameters and compare that with the previous version. Remember the best.

Then you only need to have an array with the best value so far, so an UNO would do. Problem is that it will converge very slowly and slower as time passes.