A Proximal-Proximal Majorization-Minimization Algorithm for Nonconvex Rank Regression Problems

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...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 71; pp. 3502 - 3517
Main Authors: Tang, Peipei, Wang, Chengjing, Jiang, Bo
Format: Journal Article
Language:English
Published: New York IEEE 2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Convergence
Criteria
Linear programming
Minimization
Nonconvex rank regression problems
Optimization
proximal point algorithm
proximal-proximal majorization-minimization algorithm
Regularization
semismooth Newton method
Signal processing algorithms
Urban areas
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2023.3315454