Can I solve this with Matlab instead of CVX?

I am using an RPCA code I got online, which contains the following CVX lines:

variable xp(p,1);
minimize norm(xp,1)
subject to 
    sum_square(yt - A*xp) <= epsilon; 

I would like to replace the CVX with Matlab Optimization Toolbox commands if possible, due to licensing issues. I have never used either CVX or the Optimization Toolbox. Could someone translate it or tell me it can’t be translated?


PS: That’s the only CVX in the app.

I do not really think this question for the CVX list but anyway I would solve

\begin{array}{lccl} \min & ||x||_1 \\ st & ||y-Ax||_2 & \leq & \sqrt{\varepsilon} \end{array}

Why square in the constraints? This is conic quadratic problem (aka. SOCP) that can be solved with MOSEK or SeDuMi.

You may want to have a look at the MOSEK modelling manual.

Finally you might be better off solving the dual problem.

Thanks. If I’d asked on Mathworks, probably nobody would know CVX.

Since I posted, we’ve hired a mathematician. I’ll point her to your suggestions.