Scalable Algorithms for the Sparse Ridge Regression

Understand

Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades.

• This work focuses on sparse ridge regression, which enforces the sparsity by use of the L0 norm.
• We first prove that the continuous relaxation of the mixed integer second order conic (MISOC) reformulation using perspective formulation is equivalent to that of the convex integer formulation proposed in recent work.
• We also show that the convex hull of the constraint system of MISOC formulation is equal to its continuous relaxation.