We propose and study new projection-type algorithms for solving pseudomonotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of the cost operators. We prove weak and strong convergence theorems for the sequences generated by these new methods. The numerical behavior of the proposed algorithms when applied to several test problems is compared with that of several previously known algorithms.

中文翻译：

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用非Lipschitz映射解决变分不等式的新算法和收敛定理

我们提出并研究了新的投影型算法，用于解决实际希尔伯特空间中的伪单调变分不等式问题，而无需假设成本算子的Lipschitz连续性。我们证明了这些新方法生成的序列的弱收敛定理和强收敛定理。将所提出的算法应用于几种测试问题的数值行为与几种先前已知的算法进行了比较。