A theorem due to Fitzpatrick provides a representation of arbitrary maximal monotone operators by convex functions. This paper explores representability of arbitrary (nonnecessarily 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. © Springer 2005.
|Publication status||Published - 1 Mar 2005|
- Convex functions
- Monotone operators