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A Parameter-Free Adaptive Reflected Gradient Method for Monotone Variational Inequalities
We analyze a one-evaluation-per-iteration method for $\mathrm{VI}(C,B)$ with monotone $L$-Lipschitz $B$: $x_{k+1}=P_C(x_k-λB(u_k))$, $u_k=x_k+θ_k(x_k-x_{k-1})+β_k(x_k-u_{k-1})$, $θ_k+β_k=1$. For constant step and summable filter ($\sum_kβ_k<\infty$) we prove weak convergence via a Lyapunov function
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