Non Linear Integer Programming

Question

I would like to know if there is a package in R handling non linear integer optimization.

\"Basically\", I would like to solve the following problem:

m

Answer 1

If it is hardly nonlinear there is no better method than brute force (you will never know if the minimum is local or if some flat-looking fragment doesn't have any narrow and deep valleys), except of course symbolic computation (which probably won't work because the function is too complicated) or soft computing, I mean things like genetic algorithms, Monte-Carlo, swarms, etc. (here you don't have a guarantee that it will find the very global minimum and because you have integer x it can be slower than brute force).