Find the exactly correct separating hyperplane of SVM when the data is not perfectly linearly separable
I think you can create a &quot;half-hard&quot; SVM problem. It will be like the hard SVM for positive labels (without the error term) but for negative example it will be the like the soft SVM (with the error term).
This wil guarantee you get the line that labels correctly all positive examples, but still tries to label as many of the negative examples as it can (and also create the largest margin it can)
You can do this twice to get both lines $l_1$ and $l_2$.