The projection is often used in solving variational inequalities. When projection onto the feasible set is not easy to calculate, the projection algorithms are replaced by the relaxed projection algorithms. However, these relaxed projection algorithms are not feasible, and to ensure the convergence of these relaxed projection algorithms, in addition to assuming some basic conditions, such as the Slater condition holds for the feasible set, the mapping is pseudomonotone and Lipschitz continuous, but also need to assume some additional conditions, which require some relationship between the mapping and the feasible set. In this paper, by replacing the projection onto the feasible set with the projection onto a ball (which changes from iteration) contained in the feasible set, a new feasible moving ball projection algorithm for pseudomonotone variational inequalities is obtained. Since the projection onto a ball has an explicit expression, this algorithm is easy to implement. At the same time, all the balls are contained in the feasible set, so the iteration points generated by this algorithm are all in the feasible set, which ensures the feasibility of this algorithm. The convergence of this algorithm is proved when the Slater condition holds for the feasible set, and the mapping is pseudomonotone and Lipschitz continuous. The fundamental difference between this moving ball projection algorithm and the previous relaxed projection algorithms lie in that the previous relaxed projection algorithms are all projected onto the half-space containing the feasible set, and this moving ball projection algorithm is projected onto a ball contained in the feasible set. In particular, this algorithm does not need to assume any additional conditions between the mapping and the feasible set. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.

投影通常用于求解变分不等式。当到可行集的投影不易计算时，投影算法被松弛投影算法取代。然而，这些松弛投影算法都是不可行的，为了保证这些松弛投影算法的收敛性，除了假设一些基本条件，例如可行集的Slater条件成立，映射是伪单调且Lipschitz连续的，还需要需要假设一些额外的条件，这些条件需要映射和可行集之间存在某种关系。在本文中，通过将可行集上的投影替换为可行集中包含的球（因迭代而变化）上的投影，得到了一种新的可行的赝单调变分不等式动球投影算法。由于球上的投影有明确的表达式，因此该算法很容易实现。同时，所有的球都包含在可行集中，因此该算法生成的迭代点都在可行集中，保证了该算法的可行性。当可行集满足Slater条件且映射伪单调且Lipschitz连续时，证明了该算法的收敛性。这种动球投影算法与之前的松弛投影算法的根本区别在于，之前的松弛投影算法都是投影到包含可行集的半空间上，并且该移动球投影算法被投影到包含在可行集合中的球上。特别是，该算法不需要在映射和可行集之间假设任何附加条件。最后，给出了一些数值例子来说明算法的有效性。