iPiano: inertial proximal algorithm for nonconvex optimization. In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a nonsmooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on nonconvex problems. The convergence result is obtained based on the Kurdyka-Łojasiewicz inequality. This is a very weak restriction, which was used to prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic algorithm is proved, and then iPiano is shown to satisfy the requirements of this theorem. Furthermore, a convergence rate is established for the general problem class. We demonstrate iPiano on computer vision problems – image denoising with learned priors and diffusion based image compression

References in zbMATH (referenced in 68 articles , 1 standard article )

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  1. Abubakar, Jamilu; Kumam, Poom; Rehman, Habib ur: Self-adaptive inertial subgradient extragradient scheme for pseudomonotone variational inequality problem (2022)
  2. Antoine, X.; Lorin, E.: Generalized fractional algebraic linear system solvers (2022)
  3. Ge, Zhili; Zhang, Xin; Wu, Zhongming: A fast proximal iteratively reweighted nuclear norm algorithm for nonconvex low-rank matrix minimization problems (2022)
  4. Latafat, Puya; Themelis, Andreas; Patrinos, Panagiotis: Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems (2022)
  5. Wang, Xianfu; Wang, Ziyuan: Malitsky-Tam forward-reflected-backward splitting method for nonconvex minimization problems (2022)
  6. Xu, Jiawei; Chao, Miantao: An inertial Bregman generalized alternating direction method of multipliers for nonconvex optimization (2022)
  7. Xu, Yangyang; Xu, Yibo; Yan, Yonggui; Chen, Jie: Distributed stochastic inertial-accelerated methods with delayed derivatives for nonconvex problems (2022)
  8. Yang, Hanmei; Lu, Jian; Zhang, Heng; Luo, Ye; Lu, Jianwei: Field of experts regularized nonlocal low rank matrix approximation for image denoising (2022)
  9. Yang, Xiaoqi; Zu, Chenchen: Convergence of inexact quasisubgradient methods with extrapolation (2022)
  10. Zhao, Yanan; Wu, Chunlin; Dong, Qiaoli; Zhao, Yufei: An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model (2022)
  11. Ahookhosh, Masoud; Hien, Le Thi Khanh; Gillis, Nicolas; Patrinos, Panagiotis: A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorization (2021)
  12. Attouch, Hedy: Fast inertial proximal ADMM algorithms for convex structured optimization with linear constraint (2021)
  13. Benning, Martin; Betcke, Marta M.; Ehrhardt, Matthias J.; Schönlieb, Carola-Bibiane: Choose your path wisely: gradient descent in a Bregman distance framework (2021)
  14. Breuß, Michael; Hoeltgen, Laurent; Radow, Georg: Towards PDE-based video compression with optimal masks prolongated by optic flow (2021)
  15. Chen, Yunmei; Liu, Hongcheng; Ye, Xiaojing; Zhang, Qingchao: Learnable descent algorithm for nonsmooth nonconvex image reconstruction (2021)
  16. Garba, Abor Isa; Abubakar, Jamilu; Sidi, Shehu Abubakar: An inertial projection and contraction scheme for monotone variational inequality problems (2021)
  17. Hu, Yaohua; Li, Chong; Meng, Kaiwen; Yang, Xiaoqi: Linear convergence of inexact descent method and inexact proximal gradient algorithms for lower-order regularization problems (2021)
  18. Wu, Zhongming; Li, Chongshou; Li, Min; Lim, Andrew: Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems (2021)
  19. Benning, Martin; Riis, Erlend Skaldehaug; Schönlieb, Carola-Bibiane: Bregman Itoh-Abe methods for sparse optimisation (2020)
  20. Gao, Xue; Cai, Xingju; Han, Deren: A Gauss-Seidel type inertial proximal alternating linearized minimization for a class of nonconvex optimization problems (2020)

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