Generalized iterative process and associated regularization for \(J\)-pseudomonotone mixed variational inequalities
type: Item
instance of: scholarly article
title: Generalized iterative process and associated regularization for \(J\)-pseudomonotone mixed variational inequalities
zbMATH Open document ID: 1170.65057
published in: Applied Mathematics and Computation
publication date: 2009-07-01T00:00:00Z
review text: The main purpose of this paper is to study a generalized iterative process and associated regularization for \(J\)-pseudomonotone mixed variational inequalities. A generalized iterative process for solving a class of variational inequalities (the mixed variational inequalities) is proposed. The author proves the weak convergence of the entire generalized iterative sequence in a \(p\)-uniformly smooth Banach space, \(p>1\) which admits a weakly sequentially continuous duality mapping. The general results are applied to the stationary filtration of an incompressible fluid governed by a discontinuous filtration law with limit gradient. The convergence of an iterative regularization method for the variational inequalities (with \(J\)-pseudomonotone operators in uniformly smooth Banach spaces under the assumption that the iterative parameter may vary from step to step is analyzed. Main result: An efficient face representation and recognition method (which combines 2DPCA with 2DLDA) is proposed. The major advantage of the proposed method is to combine the optimal reconstruction information from 2DPCA and the optimal discriminative information form 2DLDA. Finally experimental results reveal that all methods perform well under the condition of minor variation of tilting, scaling and rotation (on ORL database). The proposed method has better recognition accuracy under the condition of varied facial expression and lighting configuration (on Yale database). Thus the author's method is more robust.
reviewed by: Jan Lovíšek
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 58E35
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76M30
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 5573814
zbMATH Keywords: uniformly smooth Banach spaces
zbMATH Keywords: variational inequalities
zbMATH Keywords: generalized iterative process
zbMATH Keywords: \(J\)-pseudomonotone operators
zbMATH Keywords: duality maps
zbMATH Keywords: stationary filtration problems
zbMATH Keywords: weak convergence
zbMATH Keywords: regularized method
zbMATH Keywords: numerical examples
author: A. M. Saddeek
describes a project that uses: ORL face
MaRDI profile type: Publication
full work available at URL: j.amc.2009.03.006
OpenAlex ID: W2088182586
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DOI: 10.1016/J.AMC.2009.03.006
description: scientific article; zbMATH DE number 5573814