Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

Abstract

In this article, we introduce a forward–backward splitting method with a new step size rule for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multi-valued vector field on a Hadamard manifold. Using a Mann, viscosity and an inertial extrapolation method, we establish a convergence result without prior knowledge of the Lipschitz constant of the underlying operator. We present some applications of our result to variational inequality problem. Finally, we present some numerical examples to demonstrate the numerical behavior of our proposed method. The result discuss in this article extends and complements many related results in the literature.

Keywords:

• Variational inclusion problem
• inertial Tseng method
• Hadamard manifold
• monotone operator
• Riemannian manifold

Mathematics Subject Classifications:

• 47H09
• 49J25
• 65K10
• 90C25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.