In solving the split variational inequality problems, very few methods have been considered in the literature and most of these few methods require the underlying operators to be co-coercive. This restrictive co-coercive assumption has been dispensed with in some methods, many of which require a product space formulation of the problem. However, it has been discovered that this product space formulation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting structure of the split variational inequality problem. In this paper, we present two new methods with inertial steps for solving the split variational inequality problems in real Hilbert spaces without any product space formulation. We prove that the sequence generated by these methods converges strongly to a minimum-norm solution of the problem when the operators are pseudomonotone and Lipschitz continuous. Also, we provide several numerical experiments of the proposed methods in comparison with other related methods in the literature.

在解决分裂变分不等式问题时，文献中很少考虑使用方法，而这些方法中的大多数都要求底层算子具有强制性。在某些方法中已经取消了这种强制性的强制性假设，其中许多方法都需要对问题进行产品空间表述。但是，已经发现这种乘积空间公式可能会在实施过程中引起一些潜在的困难，并且其方法可能无法完全利用分裂变分不等式问题的吸引人的分裂结构。在本文中，我们提出了两种带有惯性步骤的新方法，用于在没有任何乘积空间公式的情况下解决实际希尔伯特空间中的分裂变分不等式问题。我们证明了当算子是伪单调和Lipschitz连续时，这些方法生成的序列会强烈收敛到问题的最小范数解。此外，与文献中的其他相关方法相比，我们提供了一些建议方法的数值实验。