A subgradient extragradient algorithm with inertial effects for solving strongly pseudomonotone variational inequalities

ABSTRACT

In this paper, we introduce a new algorithm by incorporating inertial terms in a subgradient extragradient algorithm for solving variational inequality problems involving strongly pseudomonotone and Lipschitz continuous operators in Hilbert spaces. The strong convergence of the algorithm is obtained under mild assumptions. We also provide some numerical examples to illustrate that the acceleration of our algorithm is effective.

KEYWORDS:

• Gradient projection
• maximal monotone operator
• inertial extrapolation
• variational inequality

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 No. 11401152].