Inertial hybrid algorithm for variational inequality problems in Hilbert spaces

Ming Tian,Bing-Nan Jiang

doi:10.1186/s13660-020-2286-1

Abstract

For a variational inequality problem, the inertial projection and contraction method have been studied. It has a weak convergence result. In this paper, we propose a strong convergence iterative method for finding a solution of a variational inequality problem with a monotone mapping by projection and contraction method and inertial hybrid algorithm. Our result can be used to solve other related problems in Hilbert spaces.

Highlights

1 Introduction The variational inequality (VI) problem plays an important role in nonlinear analysis and optimization
Based on the work above, we propose an inertial hybrid method for finding a solution of a variational inequality problem with a monotone mapping
3 Main result we propose a strong convergence algorithm for finding a solution of a variational inequality problem

Summary

Introduction

The variational inequality (VI) problem plays an important role in nonlinear analysis and optimization. Based on the work above, we propose an inertial hybrid method for finding a solution of a variational inequality problem with a monotone mapping. Lemma 2.9 ([17, 18]) Let A : H → 2H be a maximal monotone mapping and r > 0. We can consider the resolvent of a maximal monotone mapping as a generalization of metric projection operator. Lemma 2.10 ([19]) Let C be a nonempty closed convex subset of a real Hilbert space H.

Constrained convex minimization problem

Conclusion