CVX formulation without for loop


#1

Hi,

I want to solve the optimization problem below without for loop for efficiency without encountering DCP problem.

\min_{A \in \Re^{p \times k}} \sum_{j=1}^{p} \| \alpha_{j} \|_{2} subject to \|D\tilde{B} - \Lambda A \|_{\infty} \leq \tau

where
A=[\alpha_{1}, \alpha_{2},...,\alpha_{k}] and \alpha \in \Re^{p}.

p tends to be very large so if I use for loop, it slows the algorithm. Thank you for your help.

Seal.


(Mark L. Stone) #2

You appear to be inconsistent between the alphas going from 1 to p in the objective, but from 1 to k in the definition of A, so I’ll let you straighten that out. Once you do (and presuming that A has been formulated without resort to a for loop), use sum(norms(A,2,dim)) , where I’ll let you figure out what dim is supposed to be in light of your apparent inconsistency.


#3

Thank you Mark. This is very helpful and saves me lots of time.