How to write this constraint in a perspective form

Nonconvex
1

I have a positive semidefinite matrix variable M with dimension N*N, and a positive scalar variable t,

variable M(N,N) complex semidefinite
variable t
…
%%constraint
real(trace(M))/t <= c;
t>=0;

The real operation is to ensure the output of the left hand side of the first constraint is a real number (maybe the real operation can be deleted but I am not sure, so I add it). The code is wrong with this constraint. But tr\left( M \right)/t is indeed a convex perspective function and this constraint is convex, so I don’t know how to revise the code so that CVX can identify it.

2

real(trace(M))<=c*t ? Assuming c is a constant.

3

Thank you for your reply. But when c is also a variable, how to solve it?

4

It is not convex if c is also a variable. In other words the function (x,y) -> x/y is not convex as a function of two variables x,y even with y>0 or similar restrictions. And neither is tr(M)/t.