Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.

中文翻译：

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两种加速双惯性算法，用于 Hadamard 流形上的变分不等式


提出了两种改进的双惯性近端点算法，用于在 Hadamard 流形设置中求解具有伪单调向量场的变分不等式问题。所提出的方法的弱收敛是在不需要 Lipschitz 连续性条件的情况下实现的。在双惯性技术和非单调自适应步长规则的帮助下，所提算法的收敛效率得到了提高。我们提出了一个数值实验，以证明所提出的算法与几种现有算法相比的有效性。结果扩展和推广了文献中的许多最新方法。