Self-Adaptive Inertial Accelerated Algorithm for Variational Inequality, Generalized Variational Inequality and Split Feasibility Problems

ABSTRACT

In this paper, we are interested in finding the common solution of variational inequality problem, generalized variational inequality problem, split feasibility problem and fixed point problem of demicontractive mapping. We propose inertial type iterative algorithm and obtain strong convergence result under certain mild conditions in the frame of real Hilbert spaces. The suggested algorithm does not require prior knowledge of operator norm and the Lipschitz constant of the associated pseudomonotone operator. This result improves and generalizes many recent results in this direction. We further give numerical experiment for supporting our main result and compare it with other existing methods.

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