Search

This paper presents the Mann-type inertial accelerated subgradient extragradient algorithm with non-monotonic step sizes for solving the split equilibrium and fixed point problems relating to pseudomonotone and Lipschitz-type continuous bifunctions and nonexpansive mappings in the framework of real Hilbert spaces. By sufficient conditions on the control sequences of the parameters of concern, the strong convergence theorem to support the proposed algorithm, which involves neither prior knowledge of the Lipschitz constants of bifunctions nor the operator norm of the bounded linear operator, is demonstrated. Some numerical experiments are performed to show the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this work, we propose a modified inertial Tseng type method for finding a solution to the monotone inclusion problem in Hilbert spaces. The strong convergence of the algorithm is guaranteed by sufficient conditions on the control sequences of related parameters. The forms of proposed algorithms for solving some important applications of the monotone inclusion problem models are provided. Also, the numerical experiments of the proposed algorithm are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified inertial extragradient algorithm with non-monotonic step sizes for approximating a common solution of the pseudomonotone equilibrium problem and the fixed point problem for the quasi-nonexpansive mapping in the framework of a real Hilbert space. Under some constraint qualifications of the scalar sequences, the strong convergence theorem of the introduced algorithm is presented by using the self-adaptive non-monotonic step size without prior information about the Lipschitz constants of bifunction. Some numerical experiments are provided to demonstrate the computational efficiency and advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]