iPiasco: inertial proximal algorithm for strongly convex optimization. In this paper, we present a forward-backward splitting algorithm with additional inertial term for solving a strongly convex optimization problem of a certain type. The strongly convex objective function is assumed to be a sum of a non-smooth convex and a smooth convex function. This additional knowledge is used for deriving a worst-case convergence rate for the proposed algorithm. It is proved to be an optimal algorithm with linear rate of convergence. For certain problems this linear rate of convergence is better than the provably optimal worst-case rate of convergence for smooth strongly convex functions. We demonstrate the efficiency of the proposed algorithm in numerical experiments and examples from image processing.

References in zbMATH (referenced in 10 articles , 1 standard article )

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  1. Dong, Qiao-Li; Gibali, Aviv; Jiang, Dan; Ke, Shang-Hong: Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery (2018)
  2. Dong, Q. L.; Cho, Y. J.; Zhong, L. L.; Rassias, Th. M.: Inertial projection and contraction algorithms for variational inequalities (2018)
  3. Dong, Qiaoli; Jiang, Dan; Cholamjiak, Prasit; Shehu, Yekini: A strong convergence result involving an inertial forward-backward algorithm for monotone inclusions (2017)
  4. Dong, Q.-L.; Gibali, A.; Jiang, D.; Tang, Y.: Bounded perturbation resilience of extragradient-type methods and their applications (2017)
  5. Shehu, Yekini; Iyiola, Olaniyi S.: Convergence analysis for the proximal split feasibility problem using an inertial extrapolation term method (2017)
  6. Chen, Caihua; Chan, Raymond H.; Ma, Shiqian; Yang, Junfeng: Inertial proximal ADMM for linearly constrained separable convex optimization (2015)
  7. Chen, Caihua; Ma, Shiqian; Yang, Junfeng: A general inertial proximal point algorithm for mixed variational inequality problem (2015)
  8. Kang, Myeongmin; Kang, Myungjoo; Jung, Miyoun: Inexact accelerated augmented Lagrangian methods (2015)
  9. Ochs, Peter; Brox, Thomas; Pock, Thomas: iPiasco: inertial proximal algorithm for strongly convex optimization (2015)
  10. Ochs, Peter; Dosovitskiy, Alexey; Brox, Thomas; Pock, Thomas: On iteratively reweighted algorithms for nonsmooth nonconvex optimization in computer vision (2015)