Weak convergence of inertial proximal algorithms with self adaptive stepsize for solving multivalued variational inequalities

Abstract

In this work, we introduce an inertial proximal algorithm for solving multivalued variational inequality problems in a real Hilbert space. By using self-adaptive and inertial techniques via proximal operators, we establish the weak convergence of the iteration sequences generated by these algorithms when the multivalued cost mappings associated with the problems are monotone and Lipschitz continuous. Moreover, we present the nonasymptotic $O(\frac{1}{k})$ convergence rate of the proposed algorithms. We also provide some numerical examples to illustrate the accuracy and efficiency of our algorithms by comparing with other recent algorithms in the literature.

Keywords:

• Multivalued variational inequality problems
• proximal operator
• Lipschitz continuous
• monotone
• self adaptive stepsize
• inertial technique

Acknowledgments

We are very grateful to the Associate Editor and two anonymous referees for their really helpful and constructive comments that helped us very much in improving the paper.

Disclosure statement

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