Assume we have the following dual Lagrangian of a quadratic program:
Maximize: $\mathcal{L}(\vec{\lambda}, \vec{\eta}) = -\frac{1}{2}(\vec{\eta} - R^\top\vec{\lambda})^\top A^{-1}(\vec{\eta} - R^\top\vec{\lambda}) - \vec{c}^\top\vec{\lambda} $
subject to:
$\vec{\lambda}\geq 0, \vec{\eta} \geq0$
Where $A^{-1}$ is block diagonal sparse symmetric positive definite matrix, $R$ is a given sparse matrix, $\vec{c}$ is an input vector.
How to efficiently solve this problem.
I know how to solve quadratic programs in matlab (using quadprog), but for this one, I do not know how will the decision variable will look like, since I have $(\vec{\eta} - R^\top\vec{\lambda})$, not a single variable.
Please let me know, if you need more details.
Thank you.