Accelerated Projection and Contraction Method for Solving Quasi- Monotone Variational Inequalities in Hilbert Spaces
Abstract
Motivated and inspired by a novel article of Tan and Li (2022) on projection and contraction method for solving variational inequalities, we introduce and study an improved and generalized version of their work. To be precise, we provide an iterative algorithm for solving variational inequalities with quasi-monotone and Lipschitz continuous operator in real Hilbert spaces. A self- adaptive stepsize is incorporated and our computation does not involve the prior information of the Lipschitz constant of the nonlinear operator. More so, a weaker assumption than sequentially weakly continuity condition is considered. A strong convergence of the proposed algorithm is established under some mild assumptions. Furthermore, some numerical examples are equally provided.
Keywords
Projection and contraction method; pseudomonotonequasimonotonesubgradient
extragradient methods.
References
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