minimize||(R+S'QS)K + S'QT||

minimize||(R+S'QS)K + S'QT|| ,where Q & R matrices are diagonal matrix whose values to be determined such that it will minimize the value of the given expression.

Answer 1

[Johan Löfberg]

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

Answer 2

[Torsten]

Maybe "quadprog", maybe "fmincon".

See which solver best fits your needs.

Best wishes

Torsten.