A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problems
This work addresses regression problems in high-dimensional settings, but it appears incremental as it builds on existing optimization methods.
The paper tackles high-dimensional nonconvex square-root-loss regression problems by introducing a proximal majorization-minimization algorithm, proving convergence to a d-stationary point and demonstrating high efficiency in numerical experiments.
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Our key idea for making the proposed PMM to be efficient is to develop a sparse semismooth Newton method to solve the corresponding subproblems. By using the Kurdyka-Łojasiewicz property exhibited in the underlining problems, we prove that the PMM algorithm converges to a d-stationary point. We also analyze the oracle property of the initial subproblem used in our algorithm. Extensive numerical experiments are presented to demonstrate the high efficiency of the proposed PMM algorithm.