Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 179, Issue 1, Pages 197-211Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-018-1351-0
Keywords
Variational inequalities; Projection; Extragradient method; Monotone mapping; Convex set
Funding
- Natural Science Basic Research Plan in Shaanxi Province of China [2017JM1014]
Ask authors/readers for more resources
In this paper, we investigate and analyze classical variational inequalities with Lipschitz continuous and monotone mapping in real Hilbert space. The projected reflected gradient method, with varying step size, requires at most two projections onto the feasible set and one value of the mapping per iteration. We modify the method with a simple structure; a weak convergence theorem for our algorithm is proved without any requirement of additional projections and the knowledge of the Lipschitz constant of the mapping. Meanwhile, R-linear convergence rate is obtained under strong monotonicity assumption of the mapping. Preliminary results from numerical experiments are performed.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available