Inertial Haugazeau's hybrid subgradient extragradient algorithm for variational inequality problems in Banach spaces

Abstract

The variational inequality problem plays an important role in nonlinear analysis and optimization. It is a generalization of the nonlinear complementarity problem. For a variational inequality problem in a Hilbert space, the extragradient algorithm with inertial effects has been studied. For a variational inequality problem in a Banach space, Nakajo introduced Haugazeau's hybrid method and Liu introduced the Halpern subgradient extragradient method. In this paper, we construct a new inertial iterative method for solving variational inequality problems in Banach spaces based on the work we mentioned above. We propose a strong convergence theorem. As applications, our result can be used to solve constrained convex minimization problems.

Keywords:

• Variational inequality problem
• extragradient algorithm
• inertial
• Banach space
• Haugazeau's hybrid method

2010 Mathematics Subject Classifications:

• 58E35
• 47H09
• 65J15

Disclosure statement

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

Additional information

Funding

This work was supported by Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China (No. 2019ASP-TJ02).