This set of exercises has the student use a QP solver to solve an SVM in R. The suggested solver is the quadprog package. The quadratic problem is given as:
From the remark about the linear SVM, $K=XX'$, $K$ is a singular matrix usually, at most rank $p$ where $X$ is $n\times p$. But the solver quadprog requires a positive definite matrix, not just PSD, in the place of $K$, as mentioned many places (and verified). Any ideas what the instructor had in mind?
I think the workaround would be to add a small number (such as 1e-7) to the diagonal elements of the matrix which is supposed to be positive definite. I am not certain about the math behind it, but the sources below, as well as my experience, suggest that this solution works.
source: https://stats.stackexchange.com/questions/179900/optimizing-a-support-vector-machine-with-quadratic-programming
source: https://teazrq.github.io/stat542/hw/HW6.pdf