Supplement to The Hessian Screening Rule

In this section we present the algorithms for efficiently updating the Hessian and its inverse (Algorithm 1) and the full algorithm for the Hessian screening method (Algorithm 2). Algorithm 1 This algorithm provides computationally efficient updates for the inverse of the Hessian. G { 1, 2,...,p } null Reset Gap-Safe set Duplicated predictors are fortunately easy to handle since they enter the model simultaneously. We have therefore opted for a different strategy. To deal with singularities and ill-conditioned Hessian matrices, we instead use preconditioning.