Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative

Fifty years of maximal monotonicity

“…There is a whole taxonomy of n-monotone operators. The definition above is the 2-monotone case while subgradients are n-monotone for all n ∈ N and are called cyclically monotone [5,12]. For instance the noncyclic rotation…”

“…The Project Independence Evaluation System (PIES) algorithm [1] in particular modeled demand via monotone operators. 5 My own introduction to monotone operators was the result of a happy mistake. In 1972 my supervisor in Oxford suggested I write my MSc thesis on a paper by Mosco.…”

The kernel average for two convex functions and its application to the extension and representation of monotone operators

“…Now suppose that g = 1 p · p , where p > 1. Then dom g = X and Theorem 2.6 yields that dom f = λ 1 33) is an immediate consequence of (32).…”

“…Monotone operators play an important role in modern optimization and analysis; see, e.g., [19,20]. The Fitzpatrick function [10] associated with A has recently turned out to be a very effective tool for analyzing A; see, e.g., [1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,21,22,23].…”

A new proof of the integrability of the subdifferential of a convex function on a Banach space

“…The main step in our proof is to show directly that a proper lower semicontinuous convex function on a Banach space differs by a constant from the Rockafellar function (see [1]) of its subdifferential. Namely, we prove the following Theorem 1.2 (Rockafellar [8,9]).…”