Diagonal Matrix constraint

I want to find a simple solution for the following optimization problem

Using CVX, I can find the solution but I need to find a solution through linear search. Would you please kindly help.

I’m not sure what you’re referring to by “linear search”, but it seems like you’re saying that you’re not having a problem with CVX. If I’m understanding this correctly, then this really isn’t a question for the forum, which is focused on issues with CVX/TFOCS software.

@mcg, I think the set of Diagonal Matrices is Convex.

Is there a way to set a constraint on the output to be diagonal matrix?

I don’t find it on Sets.

CVX variables can be declared to be diagonal http://cvxr.com/cvx/doc/basics.html#variables .Does that do what you want?

Hi @Mark_L_Stone, It seems it should.

I will try.

Thank You.