The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.

中文翻译：

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求解变分不等式问题和不动点问题的粘性型惯性超梯度算法

本文提出了两种惯性粘性型超梯度算法，用于寻找涉及单调和 Lipschitz 连续算子的变分不等式问题和在实 Hilbert 空间中具有反收缩映射的不动点问题的通用解。我们的算法使用一个简单的步长规则，该规则由每次迭代时的一些计算生成。在没有算子的 Lipschitz 常数的先验知识的情况下，获得了两个强收敛定理。报告了所提出算法在一些数值实验中的数值行为，并与以前已知的算法进行了比较。