Hilbert空间中关于平衡与不动点问题的粘滞次外梯度算法

On Viscosity Subgradient Extragradient Methods for Equilibrium and Fixed Point Problems in Hilbert Spaces

本文将Hilbert空间中关于平衡与不动点问题的Halpern次外梯度算法推广到粘滞次外梯度算法,并且证明由该算法产生的迭代序列强收敛到两个集合的公共点,这两个集合分别是伪单调平衡问题的解集和一个demi-压缩映射的不动点集.我们的结果提升和统一了一些相关结论.

In this paper, we generalize the Halpern subgradient extragradient method to the viscosity subgradient extragradient method. We prove that the iterative sequence generated by the method strongly converges a common element of the fixed points set of a demicontractive mapping and the solutions set of an equilibrium problem for a pseudo-monotone, Lipschitz-type continuous bifunction, which solves a variational inequality for a strongly monotone and Lipschitz continuous mapping in Hilbert spaces. Our results improve and unify the corresponding results announced by some others.