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.

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  1. Abubakar, Jamilu; Kumam, Poom; Rehman, Habib ur: Self-adaptive inertial subgradient extragradient scheme for pseudomonotone variational inequality problem (2022)
  2. Labarre, Florian; Maingé, Paul-Emile: First-order frameworks for continuous Newton-like dynamics governed by maximally monotone operators (2022)
  3. Ogwo, G. N.; Izuchukwu, C.; Shehu, Y.; Mewomo, O. T.: Convergence of relaxed inertial subgradient extragradient methods for quasimonotone variational inequality problems (2022)
  4. Shehu, Yekini; Iyiola, Olaniyi S.: Weak convergence for variational inequalities with inertial-type method (2022)
  5. Xu, Yangyang; Xu, Yibo; Yan, Yonggui; Chen, Jie: Distributed stochastic inertial-accelerated methods with delayed derivatives for nonconvex problems (2022)
  6. Chao, M. T.; Zhang, Y.; Jian, J. B.: An inertial proximal alternating direction method of multipliers for nonconvex optimization (2021)
  7. Garba, Abor Isa; Abubakar, Jamilu; Sidi, Shehu Abubakar: An inertial projection and contraction scheme for monotone variational inequality problems (2021)
  8. Iyiola, Olaniyi S.; Shehu, Yekini: New convergence results for inertial Krasnoselskii-Mann iterations in Hilbert spaces with applications (2021)
  9. Izuchukwu, Chinedu; Shehu, Yekini: New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity (2021)
  10. 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)
  11. Shehu, Yekini: Linear convergence for quasi-variational inequalities with inertial projection-type method (2021)
  12. Shehu, Yekini; Vuong, Phan Tu; Zemkoho, Alain: An inertial extrapolation method for convex simple bilevel optimization (2021)
  13. Vuong, Phan Tu: A second order dynamical system and its discretization for strongly pseudo-monotone variational inequalities (2021)
  14. Fan, Jingjing; Liu, Liya; Qin, Xiaolong: A subgradient extragradient algorithm with inertial effects for solving strongly pseudomonotone variational inequalities (2020)
  15. Gao, Xue; Cai, Xingju; Han, Deren: A Gauss-Seidel type inertial proximal alternating linearized minimization for a class of nonconvex optimization problems (2020)
  16. Jolaoso, Lateef O.; Mewomo, Oluwatosin T.: Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm. (2020)
  17. Kang, Myeongmin: Approximate versions of proximal iteratively reweighted algorithms including an extended IP-ICMM for signal and image processing problems (2020)
  18. Loizou, Nicolas; Richtárik, Peter: Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods (2020)
  19. Shehu, Yekini; Gibali, Aviv; Sagratella, Simone: Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces (2020)
  20. Shehu, Yekini; Li, Xiao-Huan; Dong, Qiao-Li: An efficient projection-type method for monotone variational inequalities in Hilbert spaces (2020)

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