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 proble...

Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems

Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems

Abstract In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation.

Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces

Abstract In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng’s extragradient method with the viscosity method together with the adaptive step size technique for finding a common solution of the investigated problem. We prove a strong convergence result for our proposed algorithm under mild conditions and without prior knowledge of the Lipschitz constant of the pseudomonotone operator in Hilbert spaces. Finally, we present some numerical experiments to show the efficiency of our method in comparison with some of the existing methods in the literature.

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Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

/pdf/inertial-shrinking-projection-algorithm-with-self-adaptive-1i5cmgj3yj.pdf

Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings

Musa A. Olona

Papers

Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings