期刊
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
卷 179, 期 1, 页码 197-211出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-018-1351-0
关键词
Variational inequalities; Projection; Extragradient method; Monotone mapping; Convex set
资金
- Natural Science Basic Research Plan in Shaanxi Province of China [2017JM1014]
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.
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