A proximal-proximal majorization-minimization algorithm for nonconvex tuning-free robust regression problems
This work addresses robust regression for statistical modeling, offering an incremental improvement in algorithmic efficiency for this domain-specific problem.
The paper tackles nonconvex tuning-free robust regression problems by introducing a proximal-proximal majorization-minimization (PPMM) algorithm, which converges to a d-stationary point and outperforms existing state-of-the-art methods in numerical experiments.
In this paper, we introduce a proximal-proximal majorization-minimization (PPMM) algorithm for nonconvex tuning-free robust regression problems. The basic idea is to apply the proximal majorization-minimization algorithm to solve the nonconvex problem with the inner subproblems solved by a sparse semismooth Newton (SSN) method based proximal point algorithm (PPA). We must emphasize that the main difficulty in the design of the algorithm lies in how to overcome the singular difficulty of the inner subproblem. Furthermore, we also prove that the PPMM algorithm converges to a d-stationary point. Due to the Kurdyka-Lojasiewicz (KL) property of the problem, we present the convergence rate of the PPMM algorithm. Numerical experiments demonstrate that our proposed algorithm outperforms the existing state-of-the-art algorithms.