Illegal Operation for Using "abs"


I am using CVX tool for solving the optimization problem below:

My code gives me an error for the illegal operation {convex} - {convex} due to absolute terms at the second and third constraints. I know that error is caused by “-abs” part since it becomes concave. I do some research and find out that it might be clarified with modelling absolute values via using binary method. However, i could not perform this method on my constraints. Are there any tips available to use it on this given two constraints?

I will be appreciated and grateful for any advice.

See section 9.1.6 “Exact absolute value” of Mosek Modeling Cookbook
“y = abs(x)” in Logics and integer-programming representations - YALMIP .

Hi Mark,

Thank you for fast response. I applied the part which you have mentioned in

However, i am getting the error as “integer constraints can not be used with SDPT3 solver.”. So, do i need the professional version of CVX for using MOSEK? Or is there any possible way to overcome this situation?

Thank you.

You can see here Solvers — CVX Users' Guide which solvers support mixed-integer.

You don’t need a different CVX version. If you have your own installation of MOSEK with its own license (for example a free personal academic license), then you can plug that into CVX.