New comer in SOCP Problem

#1

Hello! This is a newcomer in CVX. Can anybody recommend some materials about how to solve SOCP problem. Here is an example.
https://sci-hub.tw/10.1016/j.sigpro.2012.03.020

We want to solve the problem in the attached paper in Eq.15. Currently, I am getting in trouble with the F-norm constraint.

It may be easy for an expert but nor for a new one.

Appreciate it very much.

(Mark L. Stone) #2

Can you enter the equation here, complete with all assumptions, explanation of notation, specification of which variables are decision (optimization) variables vs. input data?

#3

Thanks, Mark. Here is the problem description.

image
In the problem, Matrix P with dimension NxQ is unknown.
r is a column vector with size N. r is actually an intermediate variable.
Es and Wopt are known matrices with dimension MxK and KxK. \Phi is also known as Mxk. \Beta is a known positive priori.
Our goal is to solve matrix P.

Thanks again for your help. If you have any questions, please feel free to post it.

Thanks.

(Mark L. Stone) #4

Ignoring hats, tilde, etc, and presuming sqrtm(Wopt) is W_{opt}^{1/2}, use
norm(E*sqrt(mWopt) - Phi*P,'fro') <= beta

I recommend you read or re-read the CVX Users’ Guide http://cvxr.com/cvx/doc/ In particular, have you read http://cvxr.com/cvx/doc/funcref.html#nonlinear ?

#5

THANKS Mark. I did read those materials. I will try according to your comments. :+1:

(Mark L. Stone) #6

I meant sqrtm(Wopt), not sqrt(Wopt).I’ve now corrected it.

#7

Is sqrtm() also a built-in function in CVX. I did not find it actually in the built-function list given by http://cvxr.com/cvx/doc/funcref.html#built-in-functions?

(Mark L. Stone) #8

sqrtm is NOT a CVX function. It is a MATLAB function which can be applied to MATLAB variables, not to CXV variables or expressions. You wrote that Wopt is a known matrix, i.e., input data., so therefore, MATLAB functions can be applied to it. I wrote
presuming sqtm(Wopt) is W_{opt}^{1/2}
because I was leaving it to you to create whatever input matrix is needed there.That has nothing to do with CVX.

#9

OK, get it. I will have a try first. Hope it works. Thanks.