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Extended auxiliary problem principle to variational inequalities involving multi-valued operators.
- Source :
- Optimization; Jun2004, Vol. 53 Issue 3, p223-252, 30p
- Publication Year :
- 2004
-
Abstract
- An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension supposes that the operator of the variational inequality is split up into the sum of a maximal monotone operator and a single-valued operator , which is linked with a sequence of non-symmetric components of auxiliary operators by a kind of pseudo Dunn property. The current auxiliary problem is constructed by fixing at the previous iterate, whereas is considered at a variable point. Using auxiliary operators of the form , the standard assumption of the strong convexity of the function h is weakened by exploiting mutual properties of and h . Convergence of the general scheme is analysed allowing that the auxiliary problems are solved approximately. Some applications are sketched briefly. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 53
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 13867790
- Full Text :
- https://doi.org/10.1080/02331930410001715532