NDLI: Maximality of the Sum of a Maximally Monotone Linear Relation and a Maximally Monotone Operator

Content Provider	Springer Nature Link
Author	Borwein, Jonathan M. Yao, Liangjin
Copyright Year	2013
Abstract	The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar’s constraint qualification holds. In this paper, we prove the maximal monotonicity of A + B provided that A, B are maximally monotone and A is a linear relation, as soon as Rockafellar’s constraint qualification holds: ${\operatorname{dom}}\,A\cap{\operatorname{int}}\,{\operatorname{dom}}\,B\neq\varnothing$ . Moreover, A + B is of type (FPV).
Starting Page	603
Ending Page	616
Page Count	14
File Format	PDF
ISSN	18770533
Journal	Set-Valued Analysis
Volume Number	21
Issue Number	4
e-ISSN	18770541
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-09-20
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Constraint qualification Convex set Fitzpatrick function Linear relation Maximally monotone operator Monotone operator Monotone operator of type (FPV) Multifunction Normal cone operator Rockafellar’s sum theorem Set-valued operator Linear relations Monotone operators and generalizations Positive operators and order-bounded operators Applications in optimization, convex analysis, mathematical programming, economics Convex programming Analysis Geometry
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Statistics and Probability Analysis Numerical Analysis

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