Abstract
In this paper we study a classical monotone and Lipschitz continuous variational inequality in real Hilbert spaces. Two projection type methods, Mann and its viscosity generalization are introduced with their strong convergence theorems. Our methods generalize and extend some related results in the literature and their main advantages are: the strong convergence and the adaptive step-size usage which avoids the need to know apriori the Lipschitz constant of variational inequality associated operator. Primary numerical experiments in finite and infinite dimensional spaces compare and illustrate the behaviors of the proposed schemes.
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Dedicated to Professor Le Dung Muu on the Occasion of his 70th Birthday.
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Gibali, A., Thong, D.V. & Tuan, P.A. Two simple projection-type methods for solving variational inequalities. Anal.Math.Phys. 9, 2203–2225 (2019). https://doi.org/10.1007/s13324-019-00330-w
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DOI: https://doi.org/10.1007/s13324-019-00330-w
Keywords
- Projection-type method
- Variational inequality
- Mann-type method
- Viscosity method
- Projection and contraction method