For mean-variance portfolio optimization with short-selling allowed, but restricted to a certain percentage of the portfolio weights (lets assume N), we can constrain it in the follwoing way:
(from j=1 to n) sum[max(-wj,0)] <= N
the problem is that it is not linear and so if we add it to our mean-variance problem formulation we will no longer have a convex quadratic program.
How would you linearize it with n new decision variables?