Go to  Advanced Search

Please note that cIRcle is currently being upgraded to DSpace v5.1. The upgrade means that the cIRcle service will not be accepting new material from 05:00 on September 1/15 until 08:00 on September 4/15. Read only access will be available during this period. Apologies for the inconvenience.

Decompositions and representations of monotone operators with linear graphs

Show full item record

Files in this item

Files Size Format Description   View
ubc_2008_spring_yao_liangjin.pdf 761.5Kb Adobe Portable Document Format   View/Open
Title: Decompositions and representations of monotone operators with linear graphs
Author: Yao, Liangjin
Degree Master of Science - MSc
Program Interdisciplinary Studies
Copyright Date: 2007
Publicly Available in cIRcle 2008-11-24
Subject Keywords Maximal montone operator; Anixymmetric operator; Decomposition; Subdifferential; Semicontinuous convex function; Matrix; Fitzpatrick function; Fenchel conjugate; Linear relations
Abstract: We consider the decomposition of a maximal monotone operator into the sum of an antisymmetric operator and the subdifferential of a proper lower semicontinuous convex function. This is a variant of the well-known decomposition of a matrix into its symmetric and antisymmetric part. We analyze in detail the case when the graph of the operator is a linear subspace. Equivalent conditions of monotonicity are also provided. We obtain several new results on auto-conjugate representations including an explicit formula that is built upon the proximal average of the associated Fitzpatrick function and its Fenchel conjugate. These results are new and they both extend and complement recent work by Penot, Simons and Zălinescu. A nonlinear example shows the importance of the linearity assumption. Finally, we consider the problem of computing the Fitzpatrick function of the sum, generalizing a recent result by Bauschke, Borwein and Wang on matrices to linear relations.
URI: http://hdl.handle.net/2429/2807
Scholarly Level: Graduate

This item appears in the following Collection(s)

Show full item record

All items in cIRcle are protected by copyright, with all rights reserved.

UBC Library
1961 East Mall
Vancouver, B.C.
Canada V6T 1Z1
Tel: 604-822-6375
Fax: 604-822-3893