線性化兩個二進制求和的平方根

$$\ displaystyle z = \ sqrt {\ lambda \ left（x + y \ right）}$$

For $$j\in\{0,1,2\}$$, introduce binary variable $$w_j$$ to indicate whether $$x+y=j$$, and then impose the following linear constraints: \begin{align} \sum_{j=0}^2 w_j &= 1 \\ \sum_{j=0}^2 j\cdot w_j &= x+y \\ \sqrt{\lambda}\sum_{j=0}^2 \sqrt{j}\cdot w_j &= z \end{align}