Two regularized inertial Tseng methods for solving inclusion problems with applications to convex bilevel programming

Abstract

Combining the inertial technique, regularization, and the Tseng method for approximating a zero of the sum of monotone operators in a real Hilbert space, we propose two regularized inertial Tseng methods for approximating a zero of the sum of two maximal monotone operators in the case where one of them is monotone and Lipschitz continuous. We establish strong convergence of the sequences generated by our algorithms and derive several interesting consequences of our results. We then apply our results to solving convex bilevel programming problems and illustrate the cost efficiency of our methods by numerically comparing them with other methods in the literature.

Keywords:

• Inclusion problem
• monotone operator
• regularization
• Tseng method
• inertial-type algorithm

Acknowledgments

Both authors are grateful to the editor and three anonymous referees for their useful comments and helpful suggestions.

Disclosure statement

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

Additional information

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion (Grant 2001893) and by the Technion General Research Fund (Grant 2016723).