A proximal-proximal majorization-minimization algorithm for nonconvex rank regression problems

Journal:IEEE Transactions on Signal Processing

Key Words:Nonconvex rank regression problems, semismooth Newton method, proximal-proximal majorization-minimization algorithm, proximal point algorithm

Abstract:In this paper, we introduce a proximal-proximal majorization-minimization (PPMM) algorithm for nonconvex rank regression problems. The basic idea of the algorithm 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). It deserves mentioning that we adopt the sequential regularization technique and design an implementable stopping criterion to overcome the singular difficulty of the inner subproblem. Especially for the stopping criterion, it plays a very important role for the success of the algorithm. Furthermore, we also prove that the PPMM algorithm converges to a stationary point. Due to the Kurdyka-Łojasiewicz (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.

Indexed by:SCI

Correspondence Author:Peipei Tang, Chengjing Wang, Bo Jiang

Volume:71

Page Number:3502-3517

Translation or Not:no

Date of Publication:2023-12-06

Included Journals:SCI