In this paper, we investigate and analyse the strong convergence of the sequence generated by an inexact proximal point method with possible unbounded errors for finding zeros of monotone operators in Hadamard spaces. We show that the boundedness of the generated sequence is equivalent to the zero set of the operator to be nonempty. In this case, we prove the strong convergence of the generated sequence to a zero of the operator. We also provide some applications of our main results and give a numerical example to show the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]
In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature. [ABSTRACT FROM AUTHOR]
The purpose of this paper is to introduce and study the existence problem of solution for a system of monotone variational inclusion problems in Hilbert spaces. By using the inertial forward-backward splitting technique, we propose and analyze an algorithm. Under suitable conditions, we proved that the sequence generated by the algorithm converges strongly to a solution of such kind of monotone variational inclusion problems. At the end of the paper, some applications are also given. The results presented in the paper extend and improve some recent results. [ABSTRACT FROM AUTHOR]