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 36 articles , 1 standard article )

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  1. Ogwo, G. N.; Izuchukwu, C.; Shehu, Y.; Mewomo, O. T.: Convergence of relaxed inertial subgradient extragradient methods for quasimonotone variational inequality problems (2022)
  2. Iyiola, Olaniyi S.; Shehu, Yekini: New convergence results for inertial Krasnoselskii-Mann iterations in Hilbert spaces with applications (2021)
  3. Jolaoso, L. O.; Alakoya, T. O.; Taiwo, A.; Mewomo, O. T.: Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space (2021)
  4. Shehu, Yekini; Vuong, Phan Tu; Zemkoho, Alain: An inertial extrapolation method for convex simple bilevel optimization (2021)
  5. Vuong, Phan Tu: A second order dynamical system and its discretization for strongly pseudo-monotone variational inequalities (2021)
  6. Fan, Jingjing; Liu, Liya; Qin, Xiaolong: A subgradient extragradient algorithm with inertial effects for solving strongly pseudomonotone variational inequalities (2020)
  7. Gao, Xue; Cai, Xingju; Han, Deren: A Gauss-Seidel type inertial proximal alternating linearized minimization for a class of nonconvex optimization problems (2020)
  8. Jolaoso, Lateef O.; Mewomo, Oluwatosin T.: Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm. (2020)
  9. Kang, Myeongmin: Approximate versions of proximal iteratively reweighted algorithms including an extended IP-ICMM for signal and image processing problems (2020)
  10. Loizou, Nicolas; Richtárik, Peter: Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods (2020)
  11. Shehu, Yekini; Gibali, Aviv; Sagratella, Simone: Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces (2020)
  12. Shehu, Yekini; Li, Xiao-Huan; Dong, Qiao-Li: An efficient projection-type method for monotone variational inequalities in Hilbert spaces (2020)
  13. Kesornprom, Suparat; Cholamjiak, Prasit: Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in Hilbert spaces with applications (2019)
  14. Ogbuisi, Ferdinard U.; Mewomo, Oluwatosin T.: Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem (2019)
  15. Shehu, Yekini: New inertial method for nonexpansive mappings (2019)
  16. Shehu, Yekini; Cholamjiak, Prasit: Iterative method with inertial for variational inequalities in Hilbert spaces (2019)
  17. Shehu, Yekini; Iyiola, Olaniyi S.; Li, Xiao-Huan; Dong, Qiao-Li: Convergence analysis of projection method for variational inequalities (2019)
  18. Stathopoulos, Giorgos; Jones, Colin N.: An inertial parallel and asynchronous forward-backward iteration for distributed convex optimization (2019)
  19. Thong, Duong Viet; Hieu, Dang Van: Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems (2019)
  20. Wu, Zhongming; Li, Min: General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems (2019)

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