Selection of the ADMM penalty parameter rho in K-ADMM

Determine a principled method for selecting the ADMM penalty parameter rho in the K-ADMM algorithm used to solve the l1-regularized universal kriging problem for real-time grid frequency forecasting, in order to achieve favorable convergence behavior and numerical conditioning.

Background

The paper develops K-ADMM, an ADMM-based solver for the l1-regularized universal kriging problem. The augmented Lagrangian introduces a penalty parameter rho that both stabilizes the ill-conditioned quadratic term and influences the convergence speed of the iterative method via the proximal penalty in the KKT system.

The authors explicitly note that the choice of rho critically affects convergence rate and numerical conditioning. They state that, in practice, rho is typically chosen using heuristic or adaptive strategies and that systematic selection remains unresolved, referring readers to the ADMM literature. This leaves open the problem of devising a principled selection rule for rho tailored to their K-ADMM scheme in this kriging setting.