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

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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).

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Authors and Affiliations

  1. CARMA, University of Newcastle, Newcastle, New South Wales, 2308, Australia

    Jonathan M. Borwein & Liangjin Yao

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  1. Jonathan M. Borwein
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  2. Liangjin Yao
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Correspondence to Liangjin Yao.

Additional information

Dedicated to Petar Kenderov on the occasion of his seventieth birthday.

J. M. Borwein was Laureate Professor at the University of Newcastle and Distinguished Professor at King Abdul-Aziz University, Jeddah.

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Borwein, J.M., Yao, L. Maximality of the Sum of a Maximally Monotone Linear Relation and a Maximally Monotone Operator. Set-Valued Var. Anal 21, 603–616 (2013). https://doi.org/10.1007/s11228-013-0259-y

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  • DOI: https://doi.org/10.1007/s11228-013-0259-y

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