How to implement a convex optimization problem in MATLAB using CVX

I have the following optimization problem,

Where, R is a known matrix and V is a (N+1)*(N+1) size positive definite matrix.

V can be defined as v'(v')^H where v'= [v^T , t]^T and v=[exp(-j phi1),exp(-j phi2)...exp(-j phiN)]^T.

I need to solve above formulated problem using CVX in matlab.

Here, (.)^T and (.)^H corresponds to transpose and hermitian respectively. And t is an auxiliary variable.

[Torsten]

Is it obvious that tr(R*V) is real-valued ?

Answer 1

[Santosh Fatale]

Hi Shankul,

I understand that you want to implement the convex optimization problem in MATLAB using cvx library.

It is my understanding that you have already installed the cvx library on your system. To learn more about implementing optimization problem using cvx library, I would recommend you go through the examples available on cvx research homepage.

Furthermore, you could explore the following MATLAB documentation page related to solving convex optimization problem using Convex Optimization Toolbox.

Convex Optimization in MATLAB