Monotone operators representable by l.s.c. convex functions
Benar Fux Svaiter | Martinez-Legaz, J-E.
monotone operators | convex functions
A theorem due to Fitzpatrick provides a representation of arbitrary maximal monotone operators by convex functions. This paper explores representability of arbitrary (non necessarily maximal) monotone operators by convex functions. In the finite dimensional case, we identify the class of monotone operators that admit a convex representation as the one consisting of intersections of maximal monotone operators and characterize the monotone operators that have a unique maximal monotone extension.