In this work, we introduce two Bregman projection algorithms with self-adaptive stepsize for solving pseudo-monotone variational inequality problem in a Hilbert space. The weak and strong convergence theorems are established without the prior knowledge of Lipschitz constant of the cost operator. The convergence behavior of the proposed algorithms with various functions of the Bregman distance are presented. More so, the performance and efficiency of our methods are compared to other related methods in the literature.

中文翻译：

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求解伪单调变分不等式问题的新 Bregman 投影方法

在这项工作中，我们介绍了两种具有自适应步长的 Bregman 投影算法，用于解决希尔伯特空间中的伪单调变分不等式问题。弱收敛定理和强收敛定理是在没有成本算子的 Lipschitz 常数的先验知识的情况下建立的。提出了具有各种布雷格曼距离函数的算法的收敛行为。更重要的是，我们的方法的性能和效率与文献中的其他相关方法进行了比较。