I want to find one method or approach or idea which compute following statement: $ \sup_{t \in [0,1]} \left( \inf_{X \in C^1([0,1])} \left\| \frac{dX(t)}{dt} - A(t)X(t) - F(t) \right\| \right) $ Thanks alot.
I want to find another idea for solving:
$\displaystyle\min\int_0^1\left(\left\|\frac{dX(t)}{dt}-A(t)X(t)-F(t)\right\|\mathrm{d}t\right) ,X(0)=X_0,X(t)\in K\subseteq\mathbb{R}^n\;,$
where $K$ is a closed interval.