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 30 articles , 1 standard article )

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  1. Ochs, Peter: Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano (2019)
  2. Bednarczuk, E. M.; Jezierska, A.; Rutkowski, K. E.: Proximal primal-dual best approximation algorithm with memory (2018)
  3. Boţ, Radu Ioan; Csetnek, Ernö Robert; Nimana, Nimit: An inertial proximal-gradient penalization scheme for constrained convex optimization problems (2018)
  4. Cazelles, Elsa; Seguy, Vivien; Bigot, Jérémie; Cuturi, Marco; Papadakis, Nicolas: Geodesic PCA versus log-PCA of histograms in the Wasserstein space (2018)
  5. Iutzeler, Franck; Malick, Jérôme: On the proximal gradient algorithm with alternated inertia (2018)
  6. Lanza, Alessandro; Morigi, Serena; Sciacchitano, Federica; Sgallari, Fiorella: Whiteness constraints in a unified variational framework for image restoration (2018)
  7. Quéau, Yvain; Durou, Jean-Denis; Aujol, Jean-François: Variational methods for normal integration (2018)
  8. Roy, Souvik; Borzì, Alfio: A new optimization approach to sparse reconstruction of log-conductivity in acousto-electric tomography (2018)
  9. Themelis, Andreas; Stella, Lorenzo; Patrinos, Panagiotis: Forward-backward envelope for the sum of two nonconvex functions: further properties and nonmonotone linesearch algorithms (2018)
  10. Wu, Chunlin; Liu, Zhifang; Wen, Shuang: A general truncated regularization framework for contrast-preserving variational signal and image restoration: motivation and implementation (2018)
  11. Zeng, Chao; Wu, Chunlin: On the edge recovery property of nonconvex nonsmooth regularization in image restoration (2018)
  12. Abergel, Rémy; Moisan, Lionel: The Shannon total variation (2017)
  13. Antoine, Xavier; Besse, Christophe; Duboscq, Romain; Rispoli, Vittorio: Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations (2017)
  14. Bonettini, S.; Loris, I.; Porta, F.; Prato, M.; Rebegoldi, S.: On the convergence of a linesearch based proximal-gradient method for nonconvex optimization (2017)
  15. Feng, Wensen; Chen, Yunjin: Speckle reduction with trained nonlinear diffusion filtering (2017)
  16. Gaviraghi, Beatrice; Annunziato, Mario; Borzì, Alfio: A Fokker-Planck based approach to control jump processes (2017)
  17. Jiang, Dandan: A multi-parameter regularization model for deblurring images corrupted by impulsive noise (2017)
  18. Stella, Lorenzo; Themelis, Andreas; Patrinos, Panagiotis: Forward-backward quasi-Newton methods for nonsmooth optimization problems (2017)
  19. Sun, Tao; Jiang, Hao; Cheng, Lizhi: Global convergence of proximal iteratively reweighted algorithm (2017)
  20. Wu, Zhongming; Li, Min; Wang, David Z. W.; Han, Deren: A symmetric alternating direction method of multipliers for separable nonconvex minimization problems (2017)

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