Another proof and a generalization of a theorem of H. H. Bauschke on monotone operators. (2nd January 2022)

• Record Type: Journal Article
• Authors: Marques Alves, M.
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 91
• Page End: 96
• Publication Date: 2022-01-02
• Subjects: Maximal monotone operators -- partial-inverse -- closedness principle -- operator splitting -- ε–enlargements; 47H05 -- 90C25 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1858833
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Using the concept of partial-inverse of monotone operators due to Spingarn, we present a new and simple proof of a result – Theorem 2 in Bauschke [A note on the paper by Eckstein and Svaiter on "General projective splitting methods for sums of maximal monotone operators". SIAM J Control Optim. 2009;48(4):2513–2515] – of Heinz H. Bauschke. Our proof is based on the maximal monotonicity of the partial-inverse and on the (asymptotic) closedness principle on the graph of maximal monotone operators in the weak × strong topology. We also present a generalization of Bauschke's theorem to the more general setting of ε –enlargements of monotone maps.