Linear objective with quadratic constraint

Hey guys!

I'm trying to solve a portfolio optimization problem with a maximum return strategy, which implies that I try to maximize the return for a given level of std.deviation. As far as I know this kind of problem involves Fmincon as optimizer.

I have used the following set up but i'm facing some challenges; http://se.mathworks.com/help/optim/ug/linear-or-quadratic-problem-with-quadratic-constraints.html?refresh=true

I would like to maximize the portfolio return s.t. to a given level of std. deviation, therefore I have done the following:

I've set Q=zero(2,2) (as I have a portfolio of two assets) and c = zero(1,1) which implies that I end up with the problem to minimize f'x (which should be negative in order to maximize it). In my constraint I have set k equal to zero and d equal to minus my maximum level of daily std. deviation.

This should as far is i'm aware do the job, but when I try to run the optimization I get the following error message:

As far as i'm aware my dimension should be fine, as my f vektor is a 2x1 which is transposed and therefor f'x is 1x1. H is a 2x2 and x should be a 2x1, which should imply that the dimension in the constraint should be fine.

I would really appreciate if someone could point out where the error lies.

I could poste the entire code, but I thought that it would be to much and that's why I referred to the link above.

Best regards,

Kristian Lunow Nielsen

Answer 1

[Torsten]

Take a look at the documentation of fmincon about the form of the functions "fun" and "nonlconstr".

Best wishes

Torsten.

Answer 2

[Steve Grikschat]

As of R2020b, Optimization Toolbox now has a dedicated solver for second-order cone programming, which can be used to solve quadratic constrained problems.

https://www.mathworks.com/help//optim/ug/convert-quadratic-constraints-to-second-order-cone-constraints.html

https://www.mathworks.com/help//optim/ug/convert-qp-to-socp.html

Function reference:

https://www.mathworks.com/help//optim/ug/coneprog.html

coupled with a function to make a second-order cone constraint

https://www.mathworks.com/help//optim/ug/optim.coneprog.secondorderconeconstraint.html

For an example see

https://www.mathworks.com/help//optim/ug/cone-programming-mass-nonlinear-spring.html