Full Text: PDF
Received December 5, 2018; Accepted July 1, 2019; Published July 12, 2019
Abstract. In this paper, we study the weak and the strong convergence of a self-adaptive Armijo-like step size method for solving variational inequality problems with monotone and Lipschitz continuous mappings in a real Hilbert space. We combine Tseng’s extragradient method with relaxation algorithm and Yamada’s algorithm, respectively. It is worth emphasizing that our algorithm do not need to know the Lipschitz constant of the Lipschitz continuous mapping. We also give numerical examples to illustrate our main results.
How to Cite this Article:
Ming Tian, Mengying Tong, A self-adaptive Armijo-like step size method for solving monotone variational inequality problems in Hilbert spaces, Journal of Nonlinear Functional Analysis, Vol. 2019 (2019), Article ID 29, pp. 1-15.