Weak and strong convergence of inertial Tseng's extragradient algorithms for solving variational inequality problems

Abstract

In this paper, we introduce two inertial Tseng's extragradient algorithms with the Armijo-like step size rule for solving variational inequality problems involving monotone and Lipschitz continuous operators. Strong and weak convergence theorems are established in Hilbert spaces. Some numerical experiments are provided to illustrate the efficiency and advantage of the proposed algorithms.

Keywords:

• Variational inequality problem
• Tseng's extragradient method
• inertial method
• relaxation algorithm
• Armijo-like step size rule

2010 Mathematics Subject Classifications:

• 49J40
• 90C52
• 47H05
• 90C26
• 47J20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This article was supported by the National Natural Science Foundation of China [grant numbers 11561049, 11471236].and established strong convergence theorems