I need to minimize a single polynomial $P(x_1,x_2,...,x_n)$ with the constraint that for each $i$, $0\leq x_i \leq 1$. The number of variables in my practical problem is at most $50$. The degree is at most $10$. The number of monomials is about 2 million.
Are there any tools that can handle such minimization problems? An approximate solution which is guaranteed to be off by some multiplicative factor would also be welcome.