Hi I have the following miniization problem
min_{||x||<=D_x} 0.5x^TQx + c^Tx + c_y||x||
such that
E[(x^s_j + \xi_j)^2]<= beta_j , j =1,…,m
where the expectation is in terms of a random variable \xi_j. Anything else is deterministic. How can I take this expectation and formulate it as a deterministic problem for CVX?
Best,
CVX doesn’t know anything about random variables or expectation. You need to do that on your own in order to come up with deterministic CONVEX constraints. That is part of your formulation of a convex optimization problem. if you can’t arrive at a suitable convex optimization pronlem, CVX is not the right tool.
If, for instance, that winds up being sum over i of p(i)*(x^s_j + \xi_j)^2), where the p(i) are probabilities summing to 1, and s_j are >= 1 and x and xi_j are >= 0 so that square_pos can be used, then CVX would accept it.