This paper investigates the efficient solution of penalized quadratic
regressions in high-dimensional settings. We propose a novel and efficient
algorithm for ridge-penalized quadratic regression that leverages the matrix
structures of the regression with interactions. Building on this formulation,
we develop an alternating direction method of multipliers (ADMM) framework for
penalized quadratic regression with general penalties, including both single
and hybrid penalty functions. Our approach greatly simplifies the calculations
to basic matrix-based operations, making it appealing in terms of both memory
storage and computational complexity.Comment: 18 page