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A proximal-proximal majorization-minimization algorithm for nonconvex tuning-free robust regression problems

arXiv 2106.13683 ↗First posted 25 Jun 2021math.OC cs.LG cs.NAcited by 0

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Abstract (arXiv)

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.

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References · 8

  1. 2016A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problemscited by 14
  2. 2014Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programscited by 10
  3. 2018Composite Difference-Max Programs for Modern Statistical Estimation Problemscited by 10
  4. 2014DC approximation approaches for sparse optimizationcited by 8
  5. 2019An asymptotically superlinearly convergent semismooth Newton augmented Lagrangian method for Linear Programmingcited by 5
  6. 2020The flare Package for High Dimensional Linear Regression and Precision Matrix Estimation in Rcited by 5
  7. 2017On efficiently solving the subproblems of a level-set method for fused lasso problemscited by 4
  8. 2019A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problemscited by 3

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