Extragradient method with a new adaptive step size for solving non-Lipschitzian pseudo-monotone variational inequalities

Thong, Duong Viet 

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The purpose of this work is to develop a new version of the extragradient method for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. First, we prove a sufficient condition for weak convergence of a proposed algorithm under relaxed assumptions. Next, under strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a Q-linear convergence rate of this algorithm. Our results improve some recent contributions in the literature on the extragradient method.



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Thong, Duong Viet