swMATH ID: 9623
Software Authors: Ochs, Peter; Chen, Yunjin; Brox, Thomas; Pock, Thomas
Description: 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
Homepage: http://arxiv.org/pdf/1404.4805v1.pdf
Keywords: nonconvex optimization; heavy-ball method; inertial forward-backward splitting; Kurdyka-{\L}ojasiewicz inequality; proof of convergence
Related Software: iPiasco; UNLocBoX; L-BFGS; SPIRAL; RecPF; Saga; Adam; BADMM; ARock; GitHub; DnCNN; Wirtinger Flow; MNIST; BM3D; TwIST; FPC_AS; PhaseLift; GESPAR; SMAC; Spearmint
Cited in: 109 Publications
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Cited by 204 Authors

11 Boţ, Radu Ioan
10 Csetnek, Ernö Robert
9 Ochs, Peter
7 Pock, Thomas
6 Bonettini, Silvia
5 Brox, Thomas
5 Rebegoldi, Simone
5 Wu, Chunlin
5 Wu, Zhongming
4 Benning, Martin
4 Patrinos, Panagiotis
4 Prato, Marco
4 Schönlieb, Carola-Bibiane
3 Chen, Yunjin
3 Dong, Qiaoli
3 Li, Min
3 Nimana, Nimit
3 Sabach, Shoham
3 Themelis, Andreas
3 Valkonen, Tuomo
2 Abubakar, Jamilu
2 Antoine, Xavier
2 Borzì, Alfio
2 Breuß, Michael
2 Cai, Xingju
2 Chao, Miantao
2 Chen, Caihua
2 Feng, Wensen
2 Gao, Xue
2 Han, Deren
2 Hoeltgen, Laurent
2 László, Csaba Szilárd
2 Li, Guoyin
2 Lu, Jian
2 Ma, Shiqian
2 Möller, Michael
2 Pong, Ting Kei
2 Porta, Federica
2 Quéau, Yvain
2 Radow, Georg
2 Ranftl, René
2 Repetti, Audrey
2 Ruggiero, Valeria
2 Stella, Lorenzo
2 Yang, Hanmei
2 Yang, Junfeng
2 Yang, Xiaoqi
2 Zeng, Chao
1 Abergel, Rémy
1 Ahookhosh, Masoud
1 Annunziato, Mario
1 Attouch, Hedy
1 Aujol, Jean-François
1 Banert, Sebastian
1 Bednarczuk, Ewa M.
1 Bégout, Pascal
1 Besse, Christophe
1 Betcke, Marta M.
1 Bigot, Jéremie
1 Bolte, Jérôme
1 Bredies, Kristian
1 Brune, Christoph
1 Burger, Martin
1 Cazelles, Elsa
1 Chan, Raymond Hon-Fu
1 Chen, Jie
1 Chen, Shenglan
1 Chen, Xue
1 Chen, Yunmei
1 Chen, Zhangyou
1 Cheng, Lizhi
1 Cho, Yeol Je
1 Chouzenoux, Emilie
1 Clason, Christian
1 Collins, Sean M.
1 Cremers, Daniel
1 Cuturi, Marco
1 Dao, Minh Ngoc
1 de Oliveira, Welington Luis
1 Dong, Xiaomei
1 Duboscq, Romain
1 Durou, Jean-Denis
1 Ehrhardt, Matthias Joachim
1 Fadili, Jalal M.
1 Fang, Changjie
1 Favaro, Paolo
1 Frankel, Pierre
1 Gao, Yiming
1 Garba, Isah Abor
1 Garrigos, Guillaume
1 Gaviraghi, Beatrice
1 Ge, Zhili
1 Geiping, Jonas
1 Gillis, Nicolas
1 He, Songnian
1 Hendrich, Christopher
1 Hien, Le Thi Khanh
1 Hintermüller, Michael
1 Hoffmann, Sebastian
1 Hu, Yaohua
...and 104 more Authors
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Cited in 44 Serials

13 SIAM Journal on Imaging Sciences
11 Journal of Mathematical Imaging and Vision
9 Journal of Global Optimization
8 Journal of Optimization Theory and Applications
7 Computational Optimization and Applications
6 SIAM Journal on Optimization
4 Inverse Problems
3 SIAM Journal on Scientific Computing
3 Set-Valued and Variational Analysis
2 Applied Mathematics and Computation
2 Journal of Computational and Applied Mathematics
2 Asia-Pacific Journal of Operational Research
2 Journal of Scientific Computing
2 Numerical Algorithms
2 Mathematical Programming. Series A. Series B
2 Journal of Inequalities and Applications
2 SIAM Journal on Mathematics of Data Science
1 Computers & Mathematics with Applications
1 Computer Physics Communications
1 Journal of Differential Equations
1 Mathematics of Operations Research
1 SIAM Journal on Numerical Analysis
1 Circuits, Systems, and Signal Processing
1 Applied Numerical Mathematics
1 International Journal of Computer Mathematics
1 Linear Algebra and its Applications
1 Computational Statistics and Data Analysis
1 Cybernetics and Systems Analysis
1 International Journal of Computer Vision
1 ETNA. Electronic Transactions on Numerical Analysis
1 Advances in Computational Mathematics
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Vietnam Journal of Mathematics
1 International Journal of Nonlinear Sciences and Numerical Simulation
1 Journal of Evolution Equations
1 Foundations of Computational Mathematics
1 Journal of Applied Mathematics and Computing
1 Thai Journal of Mathematics
1 Acta Numerica
1 Optimization Letters
1 Science China. Mathematics
1 EURO Journal on Computational Optimization
1 International Journal of Applied and Computational Mathematics
1 Minimax Theory and its Applications

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