You haven't defined which norm you want to use. As you've tagged it with YALMIP, this is the YALMIP code for, e.g., 2-norm.
Q = diag(sdpvar(n,1));
R = diag(sdpvar(n,1));
optimize([],norm((R+S'*Q*S)*K + S'*Q*T,2))
The Frobenious norm ('fro') can be solved analytically if you want, as it is a simple quadratic expression
