Looking to solve the following MINLP, which essentially maximizes the odds of a given portfolio of 11 normally distributed, dependent stocks reaching a ceiling performance:
$$Maximize: \frac{t-M}{\Sigma}$$ $$ M = \sum_{i=0}x_i*\mu_i $$ $$ \Sigma = \sqrt{\sum_{i=0}\sum_{j=0}2*Cov(i,j)*x_i*x_j + \sum_{i=0}x_i*\sigma_i^2} $$ $$ \sum_{i=0}x_i*cost_i <= 100000 $$ $$ \sum_{i=0}x_i <=11 $$
$x_i$ is a binary variable. Is there any way to linearize this? To make it any simpler? Once the set reaches really any size, I've had trouble getting it to run at all on pyscipopt.