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


References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Bonettini, S.; Loris, I.; Porta, F.; Prato, M.; Rebegoldi, S.: On the convergence of a linesearch based proximal-gradient method for nonconvex optimization (2017)
  2. Jiang, Dandan: A multi-parameter regularization model for deblurring images corrupted by impulsive noise (2017)
  3. Stella, Lorenzo; Themelis, Andreas; Patrinos, Panagiotis: Forward-backward quasi-Newton methods for nonsmooth optimization problems (2017)
  4. Sun, Tao; Jiang, Hao; Cheng, Lizhi: Global convergence of proximal iteratively reweighted algorithm (2017)
  5. Bonettini, S.; Porta, F.; Ruggiero, V.: A variable metric forward-backward method with extrapolation (2016)
  6. Boţ, Radu Ioan; Csetnek, Ernö Robert: An inertial Tseng’s type proximal algorithm for nonsmooth and nonconvex optimization problems (2016)
  7. Feng, Wensen; Qiao, Hong; Chen, Yunjin: Poisson noise reduction with higher-order natural image prior model (2016)
  8. Plonka, Gerlind; Hoffmann, Sebastian; Weickert, Joachim: Pseudo-inverses of difference matrices and their application to sparse signal approximation (2016)
  9. Pock, Thomas; Sabach, Shoham: Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems (2016)
  10. Bégout, Pascal; Bolte, Jér^ome; Jendoubi, Mohamed Ali: On damped second-order gradient systems (2015)
  11. Ochs, Peter; Brox, Thomas; Pock, Thomas: iPiasco: inertial proximal algorithm for strongly convex optimization (2015)
  12. Ochs, Peter; Chen, Yunjin; Brox, Thomas; Pock, Thomas: iPiano: inertial proximal algorithm for nonconvex optimization (2014)