Compare $\min_{x_1} \min_{x_2} f(x_1, x_2)$ vs $\min_{x_2} \min_{x_1} f(x_1, x_2)$
Does the equation $\displaystyle min_{x,y} f(x,y)=min_{y}min_{x}f(x,y)=min_{x}min_{y}f(x,y)$ always hold for a minimization problem?