Mean-Variance Optimization, constraint as matrix operation

Hi, I am trying to use the linprog function to solve the mean-variance problem. I am confused with the input of constraint format. Basically, the objective function is

min W' * cov * W

subject to

W' *  u = targetMean
W' * vectorOne  = 1

I checked out the syntax

x = linprog(f,A,b,Aeq,beq)

I wonder how would I put the x-transpose into the constraint. Thanks.

Answer 1

[John D'Errico]

Strictly impossible using linprog. PERIOD. EVER.

Your objective function is a quadratic form. It is NOT linear.

However, nothing stops you from employing quadprog, which is designed to solve for a minimum of a quadratic form. You will have two equality constraints, so Aeq will be an array with two rows.

[Jovos]

Hey, thanks for that. I read through the documentation of quadprog. So I just set H as the co-variance matrix, set f empty. However, I am still confused how to set Aeq and beq. The constraint is

W' *  u = targetMean
W' * vectorOne  = 1

I tried to move u to the right hand side of the equation, putting 1 into Aeq and targetMean.* (u.^-1) into eb, but that does not work at all. May you elaborate a bit more? Thanks again.