Linearization of $\sum_k (y_{k}^2+x_k\,y_k)$

Question

How can I linearize $\sum_{k} (y_{k}^2+x_k\,y_k)$? when $y$ is a variable and $y\ge0$, and $x$ is a binary variable.

Answer 1

You can linearize the $x_k y_k$ exactly: https://or.stackexchange.com/questions/39/how-to-linearize-the-product-of-a-binary-and-a-non-negative-continuous-variable?r=SearchResults

But for the linearization of $y_k^2$ you’ll have to settle for an approximation: https://or.stackexchange.com/questions/180/how-to-linearize-the-product-of-two-continuous-variables?r=SearchResults