Yekini Shehu, Jeremiah N. Ezeora, Weak and linear convergence of a generalized proximal point algorithm with alternating inertial steps for a monotone inclusion problem
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Volume 5, Issue 6, 1 December 2021, Pages 881-892
Abstract. The proximal point algorithm (PPA) is a powerful tool for solving monotone inclusion problems. Recently, Tao and Yuan [On the optimal linear convergence rate of a generalized proximal point algorithm, J. Sci. Comput. 74 (2018), 826-850] proposed a generalized PPA (GPPA) for finding a zero point of a maximal monotone operator, and obtained the linear convergence rate of the generalized PPA. In this paper, we consider accelerating the GPPA with the aid of the inertial extrapolation. We propose a generalized proximal point algorithm with alternating inertial steps solving monotone inclusion problem, and obtain weak convergence results under some mild conditions. When the inverse of the involved monotone operator is Lipschitz continuous at the origin, we prove that the iterative sequence generated by our generalized proximal point algorithm is linearly convergent. The Fejér monotonicity of even subsequences of the iterative sequence is also recovered. Finally, we give some priori and posteriori error estimates of our generated sequences.
How to Cite this Article:
Yekini Shehu, Jeremiah N. Ezeora, Weak and linear convergence of a generalized proximal point algorithm with alternating inertial steps for a monotone inclusion problem, J. Nonlinear Var. Anal. 5 (2021), 881-892.