Given two pairs of vector (U, V) and $(U_1, V_1)$ where U, V, $U_1$, $V_1$ have the same length K, $U_1$ and $V_1$ are constant vectors. Is it possible to say that minimizing $\|U-U_1 \|^2$ + $\|V-V_1 \|^2$ is equivalent to minimize $(U^TV-U^T_1V_1)^2$ ? If it's possible, how to prove it ?
PS: Some comments below point out that we cannot have the way from second expression to the first expression. Can we prove minimizing the first expression => minimize the second one ?