三步投影方法的广义收敛及其在变分不等式中的应用(英文)

General convergence analysis for three-step projection Methods and applications to Variational problems

在这篇文章中,首先介绍了带有误差估计的三步投影法的广义模型,其次将其应用到解决一组在Hilbert空间中的非线性变分不等式的近似解。令H是实值Hilbert空间,K是H中的非空闭凸集。对任意选定的起始点x0,y0,z0∈K,计算序列｛xn｝,｛yn｝and｛zn｝,使得xn1=(1-an-dn)xn+anPk[zn-ρT(zn)]+dnunforρ>0Yn=(1-bn-en)xn+bnPk[xn-ηT(xn)]+enνnforη>0zn=(1-cn-fn)xn+cnPκ[yn-λT(yn)]+fnwnforλ>0其中T:K→H是K上的非线性映射,PK是H到K的投影且o≤an,bn,cn,dn,en,fn≤1,｛un｝,｛vn｝,｛wn｝是K中的有界序列。三步投影模型应用到许多变分不等式问题。

In this paper, first we introduce a projection methods and second it has been applied general model with error estimate for three-step to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting .Let H be a real Hilbert space and K be a nonempty closed convex subset of H .For arbitrarily chosen initial points xo,y0,z0∈K, compute sequences {xn},{yn} and {zn} such that x（n＋1）=（1-an-dn）xn＋anPk[zn-ρT（zn）]＋dnun for ρ〉0 yn=（1-bn-en）xn＋bnPK[xn-ηT（xn）]＋envn for η〉0 zn=（1-cn-fn）xn＋cnPK[yn-λT（yn）]＋fnwn forλ〉0 where T：K→H is a nonlinear mapping on K, PK is the projection of H onto K, and 0≤an,bn,cn,dn,en,fn≤1,{un},{vn},{wn} are bounded sequences of K. The three-step model is applied to some variational inequality problems.