A Convex-Analytical Approach to Extension Results for n -Cyclically Monotone Operators |
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Authors: | Heinz H Bauschke and Xianfu Wang |
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Institution: | (1) Mathematics, Irving K. Barber School, UBC Okanagan, Kelowna, British Columbia, V1V 1V7, Canada |
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Abstract: | Results concerning extensions of monotone operators have a long history dating back to a classical paper by Debrunner and
Flor from 1964. In 1999, Voisei obtained refinements of Debrunner and Flor’s work for n-cyclically monotone operators. His proofs rely on von Neumann’s minimax theorem as well as Kakutani’s fixed point theorem.
In this note, we provide a new proof of the central case of Voisei’s work. This proof is more elementary and rooted in convex
analysis. It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.
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Keywords: | convex analysis cyclic monotonicity Debrunner– Flor extension Fenchel– Rockafellar duality Fitzpatrick functions monotone operator |
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