Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems

Zhongming Wu (), Chongshou Li (), Min Li () and Andrew Lim ()
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Zhongming Wu: Nanjing University of Information Science and Technology
Chongshou Li: National University of Singapore
Min Li: Nanjing University
Andrew Lim: National University of Singapore

Journal of Global Optimization, 2021, vol. 79, issue 3, No 4, 617-644

Abstract: Abstract This paper proposes an inertial Bregman proximal gradient method for minimizing the sum of two possibly nonconvex functions. This method includes two different inertial steps and adopts the Bregman regularization in solving the subproblem. Under some general parameter constraints, we prove the subsequential convergence that each generated sequence converges to the stationary point of the considered problem. To overcome the parameter constraints, we further propose a nonmonotone line search strategy to make the parameter selections more flexible. The subsequential convergence of the proposed method with line search is established. When the line search is monotone, we prove the stronger global convergence and linear convergence rate under Kurdyka–Łojasiewicz framework. Moreover, numerical results on SCAD and MCP nonconvex penalty problems are reported to demonstrate the effectiveness and superiority of the proposed methods and line search strategy.

Keywords: Nonconvex; Nonsmooth; Inertial proximal gradient method; Bregman regularization; Kurdyka–Łojasiewicz property; Global convergence (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-020-00943-7

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