首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Regularization of Nonlinear Ill-Posed Variational Inequalities and Convergence Rates
Authors:Fengshan Liu and M Zuhair Nashed
Institution:(1) Department of Mathematics and Computer Science, Delaware State University, Dover, DE, 19901, U.S.A.;(2) Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, U.S.A.
Abstract:Let H be a Hilbert space and K be a nonempty closed convex subset of H. For f isin H, we consider the (ill-posed) problem of finding u isin K for which ge 0 for all v isin K, where A : H rarr H is a monotone (not necessarily linear) operator. We study the approximation of the solutions of the variational inequality by using the following perturbed variational inequality: for fdelta isin H, Verbar fdelta – f Verbar le delta, find uepsidelta, eegr isin Keegr for which delta, eegr + epsi uepsidelta, eegr – fdelta, v – uepsidelta, eegr> ge 0 for all v isin Keegr, where epsi, delta, and eegr are positive parameters, and Keegr, a perturbation of the set K, is a nonempty closed convex set in H. We establish convergence and a rate O(epsi1 / 3) of convergence of the solutions of the regularized variational inequalities to a solution of the original variational inequality using the Mosco approximation of closed convex sets, where A is a weakly differentiable inverse-strongly-monotone operator.
Keywords:variational inequality  inverse ill-posed problem  monotone operator  degree of ill-posedness  nonlinear  convex set
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号