In this paper, strongly pseudomonotone quasi-variational inequalities are investigated. We provide sufficient conditions for existence and uniqueness of solutions of strongly pseudomonotone quasi-variational inequalities. We present some error bounds in terms of residual and regularized gap functions. The global exponential stability of equilibrium solutions of a projected dynamical system for strongly pseudomonotone quasi-variational inequalities is investigated. Strong convergence and error estimates for sequence generated by the (modified) gradient projection method with suitable choices of stepsizes are also studied. Some examples and numerical experiments are provided to support our main results.

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关于强伪单调拟变分不等式的一些结果

本文研究了强伪单调拟变分不等式。我们为强伪单调拟变分不等式的解的存在和唯一性提供了充分的条件。我们根据残差和正规间隙函数给出了一些误差范围。研究了拟伪单调拟变分不等式投影动力系统平衡解的全局指数稳定性。还研究了由（修改的）梯度投影方法生成的序列的强收敛性和误差估计，以及适当的步长选择。提供了一些示例和数值实验来支持我们的主要结果。