The generalized set-valued strongly nonlinear implicit variational inequalities
type: Item
instance of: scholarly article
title: The generalized set-valued strongly nonlinear implicit variational inequalities
zbMATH Open document ID: 0945.47043
DOI: 10.1016/S0898-1221(99)00123-6
author: Yayong Tang
author: Nan-Jing Huang
author: Ya-Ping Liu
author: Minru Bai
publication date: 2000-01-20T00:00:00Z
review text: A class of generalized set-valued strongly nonlinear implicit variational inequalities of the following type in a real Hilbert space \(H\) is studied: \[ \begin{gathered} u \in H,\;y \in Tu,\;z \in Au, \\ (gv-gu,N(y,z)) \geq f(u)-f(v) \;\text{ for all }v \in H. \end{gathered} \] Here \(g:H\to H\), \(f:H\to R\cup \{+\infty\}\), \(N:H\times H \to H\) are single-valued mappings, \(T,\;A:H\to 2^H\) are set-valued mappings. By a suitable choice of the mappings, a number of usual classes of variational inequalities and complementarity problems can be obtained. Some particular cases are briefly mentioned. An algorithm for solving the general problem mentioned by using the auxiliary principle technique of Glowinski, Lions and Tremolieres is given. Particularly, the convergence of the corresponding iterative solutions and the existence of solutions to the original problem is proved.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1391572
zbMATH Keywords: generalized set-valued strongly nonlinear implicit variational inequality
zbMATH Keywords: algorithm
zbMATH Keywords: existence
zbMATH Keywords: convergence
zbMATH Keywords: complementarity problems
reviewed by: Milan Kučera
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 1391572