New accelerated splitting algorithm for monotone inclusion problems

Jolaoso, Lateef O., Shehu, Yekini and Xu, Hong-Kun (2023) New accelerated splitting algorithm for monotone inclusion problems. Optimization. (doi:10.1080/02331934.2023.2267065).

Record type: Article

Abstract

Forward-reflected-backward splitting algorithm with inertial extrapolation of two inertial effects to find a zero of the sum of a maximal monotone and a Lipschitz continuous monotone operator is studied in this paper. The incorporation of two inertial effects on the extrapolation step is to further improve the convergence speed of the forward-reflected-backward splitting algorithm with one inertial effect extrapolation already proposed in the literature. The parameter of the second inertial effect of our proposed algorithm is chosen to be non-positive. Weak, strong, and linear convergence results are obtained under standard conditions in Hilbert spaces. Preliminary numerical illustrations show that our proposed algorithm is competitive with other related algorithms in the literature.

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Accepted/In Press date: 30 September 2023

e-pub ahead of print date: 9 October 2023

Keywords: Forward-reflected-backward splitting algorithm, Hilbert spaces, Maximal monotone operators, Two inertial effects, Weak and strong convergence, 68Q25, two inertial effects, maximal monotone operators, hilbert spaces, 90C30, 90C25, weak and strong convergence, 49M25, 90C60

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