CART Gini cost function

How is CART impurity cost function minimized?
$$J(k,t_k) = \frac{m_{left}}{m}G_{left}+\frac{m_{right}}{m}G_{right}$$
where
$$G_{left/right}$$ measures the impurity of the left/right subset
and
$$m_{left/right }$$ is the number of instances in the left/right subset$$
So how to minimize it? Should I try all possible feature values linearly and calculclate loss function for each of them?

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