一类新型变分包含问题的扰动算法和稳定性

Perturbed Algorithm and Stability of a New Variational Inclusion

引入了一类新的含(h,η)-单调算子和α-h-强单调算子的广义非线性混合拟变分包含,并建立了关于(h,η)-单调算子的广义图像收敛理论。依据广义图像收敛理论,并应用关于h,η-单调算子的预解算子技巧,作者提出了一种新的扰动迭代算法来解这类变分不等式。进而。研究了这类算法的收敛性和稳定性。结果是新的。并推广和统一了近期文献中的一些相关结论。

In this paper, we introduce a new generalized nonlinear mixed quasi-variational inclusion involving （h,η）-monotone mappings and a-h-strongly monotone mappings, and establish the generalized-graph-convergence theory about （h, η）- monotone mappings. Based on the generalized-graph-convergence theory, by using the resolvent operator technique about（ h,η） -monotone mappings, we suggest a new perturbed iterative algorithm to compute approximate solutions of this class of variational inequality. Further-more , we also discuss the convergence and stability of the perturbed algorithm. Our results are new, unify and generalize some corresponding results in recent literatures.