Existence and algorithm of solutions for nonlinear mixed variational-like inequalities in Banach spaces.
type: Item
instance of: scholarly article
title: Existence and algorithm of solutions for nonlinear mixed variational-like inequalities in Banach spaces.
zbMATH Open document ID: 1040.65053
DOI: 10.1016/S0377-0427(03)00421-7
published in: Journal of Computational and Applied Mathematics
publication date: 2003-08-25T00:00:00Z
review text: A new class of nonlinear mixed variational-like inequalities in reflexive Banach spaces is introduced. It extends previous results obtained in Hilbert spaces by \textit{X. P. Ding} [J. Sichuan Norm. Univ., Nat. Sci. 22, No. 5, 494--503 (1999; Zbl 0965.49010)], \textit{N. J. Huang} and \textit{C. X. Deng} [J. Math. Anal. Appl. 256, 345--359 (2001; Zbl 0972.49008)]. The existence and the uniqueness of the solution is proved by applying a minimax inequality due to the author. By using a new auxiliary variational-like inequality technique, a general iterative algorithm to compute approximate solutions is developed. A convergence criterion of that algorithm is also given.
reviewed by: Viorel Arnăutu
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 1970755
zbMATH Keywords: nonlinear mixed variational-like inequality
zbMATH Keywords: minimax inequality
zbMATH Keywords: auxiliary variational principle
zbMATH Keywords: general algorithm
zbMATH Keywords: reflexive Banach space
zbMATH Keywords: iterative algorithm
zbMATH Keywords: convergence
author: Xieping Ding
MaRDI profile type: Publication
cites work: Iterative schemes for solving mixed variational-like inequalities
cites work: On the generalized nonlinear variational-like inequality in reflexive Banach space
cites work: Auxiliary problem principle extended to variational inequalities
cites work: Some remarks on variational-like and quasivariational-like inequalities
cites work: General algorithm of solutions for nonlinear variational inequalities in Banach space
cites work: General algorithm for nonlinear variational-like inequalities in reflexive Banach spaces
cites work: Algorithm of solutions for mixed nonlinear variational-like inequalities in reflexive Banach space
cites work: Q4489649
cites work: General algorithm of random solutions for random nonlinear variational inequalities in banach Spaces*
cites work: A minimax inequality with applications to existence of equilibrium point and fixed point theorems
cites work: Existence and uniqueness of solutions for a general nonlinear variational inequality
cites work: Q4746741
cites work: Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
cites work: Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities
cites work: Q4010396
cites work: The nonlinear complementarity problem, with applications. I
cites work: Q3905599
cites work: Q4346042
cites work: General variational inequalities
cites work: Mixed variational inequalities
cites work: On nonlinear variational inequalities
cites work: An iterative algorithm for nonlinear variation inequalities
cites work: General algorithm for variational inequalities
cites work: General algorithm and sensitivity analysis for variational inequalities
cites work: Nonconvex functions and variational inequalities
cites work: Q4379284
cites work: A variational-like inequality problem
cites work: On generalized variational-like inequalities
cites work: Q4303388
cites work: Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
cites work: On generalized variational inequalities involving relaxed Lipschitz and relaxed monotone operators
cites work: Existence of generalized variational inequalities
cites work: Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities
full work available at URL: s0377-0427(03)00421-7
OpenAlex ID: W2159935312
description: scientific article; zbMATH DE number 1970755