Perturbed proximal point algorithms for generalized quasivariational inclusions
type: Item
instance of: scholarly article
title: Perturbed proximal point algorithms for generalized quasivariational inclusions
zbMATH Open document ID: 0902.49010
author: Xieping Ding
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-12-03T00:00:00Z
review text: The following problem has been considered: Find \(x\in H\), \(u\in T(x)\) and \(v\in A(x)\) such that \(g(x)\in\text{dom }\partial \phi(\cdot, x)\) and \[ (u- v, y- f(x))\geq \phi(g(x), x)- \phi(y,x),\quad \forall y\in H, \] where \(H\) is a Hilbert space, \(T, A: H\to 2^H\) are multivalued mappings satisfying appropriate conditions of Lipschitz continuity and strong monotonicity, \(\phi(\cdot, y): H\to\mathbb{R}\cup \{+\infty\}\) is proper convex and lower semicontinuous for each fixed \(y\in H\). On the basis of some properties of the resolvent operator associated with a maximal monotone mapping the iterative algorithm for finding solutions of the corresponding quasivariational inequality problems has been constructed. The convergence of this algorithm has been shown under strong hypotheses that are rather difficult to be checked in the case of important practical problems.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 1031637
zbMATH Keywords: generalized quasivariational inequality
zbMATH Keywords: iterative algorithm
reviewed by: Z. Naniewicz
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5370
OpenAlex ID: W2065208209
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DOI: 10.1006/JMAA.1997.5370
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description: scientific article; zbMATH DE number 1031637