iPiano
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
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References in zbMATH (referenced in 39 articles , 1 standard article )
Showing results 1 to 20 of 39.
Sorted by year (- Banert, Sebastian; Bot, Radu Ioan: A general double-proximal gradient algorithm for d.c. programming (2019)
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- Ochs, Peter: Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano (2019)
- Tan, Pauline; Pierre, Fabien; Nikolova, Mila: Inertial alternating generalized forward-backward splitting for image colorization (2019)
- Valkonen, Tuomo: Block-proximal methods with spatially adapted acceleration (2019)
- Wu, Zhongming; Li, Min: General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems (2019)
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- Benning, Martin; Burger, Martin: Modern regularization methods for inverse problems (2018)
- Boţ, Radu Ioan; Csetnek, Ernö Robert; Nimana, Nimit: An inertial proximal-gradient penalization scheme for constrained convex optimization problems (2018)
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- Iutzeler, Franck; Malick, Jérôme: On the proximal gradient algorithm with alternated inertia (2018)
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- Quéau, Yvain; Durou, Jean-Denis; Aujol, Jean-François: Variational methods for normal integration (2018)
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- Roy, Souvik; Borzì, Alfio: A new optimization approach to sparse reconstruction of log-conductivity in acousto-electric tomography (2018)
- Themelis, Andreas; Stella, Lorenzo; Patrinos, Panagiotis: Forward-backward envelope for the sum of two nonconvex functions: further properties and nonmonotone linesearch algorithms (2018)
- Wu, Chunlin; Liu, Zhifang; Wen, Shuang: A general truncated regularization framework for contrast-preserving variational signal and image restoration: motivation and implementation (2018)
- Zeng, Chao; Wu, Chunlin: On the edge recovery property of nonconvex nonsmooth regularization in image restoration (2018)