Sum theorems for maximally monotone operators of type (FPV)

Title: Sum theorems for maximally monotone operators of type (FPV)
Creator: Borwein, Jonathan M.; Yao, Liangjin
Relation: Journal of the Australian Mathematical Society Vol. 97, Issue 1
Publisher Link: http://dx.doi.org/10.1017/S1446788714000056
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2014
Description: The most important open problem in monotone operator theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds. In this paper, we establish the maximal monotonicity of A + B provided that A and B are maximally monotone operators such that star(dom A) ∩ int dom B ≠ ∅, and A is of type (FPV). We show that when also dom A is convex, the sum operator A + B is also of type (FPV). Our result generalizes and unifies several recent sum theorems.
Subject: constraint qualification; convex function; convex set; Fitzpatrick function; linear relation; maximally monotone operator; operator of type (FPV); sum problem
Identifier: http://hdl.handle.net/1959.13/1305352
Identifier: uon:21030
Identifier: ISSN:1446-7887
Language: eng
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