Asplund Decomposition of Monotone Operators
Jonathan Michael Borwein, Herre Wiersma · SIAM Journal on Optimization · 2007
We establish representations of a monotone mapping as the sum of a maximal subdifferential mapping and a “remainder” monotone mapping, where the remainder is “acyclic” in the sense that it contains no nontrivial subdifferential component. This is the nonlinear analogue of a skew linear operator. Examples of indecomposable and acyclic operators are given. In particular, we present an explicit nonlinear acyclic operator.