广义非凸变分不等式系统的松弛迭代算法

Relaxation iterative algorithm for system of general nonconvex variational inequalities

考虑定义在Hlibert空间中一致临近正则集上的广义非凸变分不等式系统问题(SGNCVIP)。建立了问题(SGNCVIP)和不动点问题之间的等价性。利用这种等价性提出了求解问题(SGNCVIP)的松弛迭代算法,进而在适当温和的条件下证明了该算法是收敛的。本文给出的结果改进并推广了相关文献中的结论。

In this paper, we introduce and consider a new system of general nonconvex variational ine- qualities defined on uniformly prox-regular sets in Hilbert spaces. We establish the equivalence be- tween the new system of general nonconvex variational inequalities and the fixed point problems. By u- sing this equivalence, we propose an relaxation iterative algorithm for solving this system and we further considered the convergence in some mild conditions. The results presented in this paper improve and extend the conclusions of the literature.