English

Malitsky-Tam forward-reflected-backward splitting method for nonconvex minimization problems

Optimization and Control 2021-11-18 v1

Abstract

We extend the Malitsky-Tam forward-reflected-backward (FRB) splitting method for inclusion problems of monotone operators to nonconvex minimization problems. By assuming the generalized concave Kurdyka-{\L}ojasiewicz (KL) property of a quadratic regularization of the objective, we show that the FRB method converges globally to a stationary point of the objective and enjoys finite length property. The sharpness of our approach is guaranteed by virtue of the exact modulus associated with the generalized concave KL property. Numerical experiments suggest that FRB is competitive compared to the Douglas-Rachford method and the Bo\c{t}-Csetnek inertial Tseng's method.

Keywords

Cite

@article{arxiv.2111.08852,
  title  = {Malitsky-Tam forward-reflected-backward splitting method for nonconvex minimization problems},
  author = {Xianfu Wang and Ziyuan Wang},
  journal= {arXiv preprint arXiv:2111.08852},
  year   = {2021}
}

Comments

24 pages

R2 v1 2026-06-24T07:41:32.771Z