TY - JOUR

T1 - Representative functions of maximally monotone
operators and bifunctions

AU - Bianchi, Monica

AU - Hadjisavvas, Nicolas

AU - Pini, Rita

PY - 2018

Y1 - 2018

N2 - The aim of this paper is to show that every representative function of a maximally
monotone operator is the Fitzpatrick transform of a bifunction corresponding
to the operator. In fact, for each representative function ϕ of the operator, there is a
family of equivalent saddle functions (i.e., bifunctions which are concave in the first
and convex in the second argument) each of which has ϕ as Fitzpatrick transform.
In the special case where ϕ is the Fitzpatrick function of the operator, the family of
equivalent saddle functions is explicitly constructed. In thiswaywe exhibit the relation
between the recent theory of representative functions, and the much older theory of
saddle functions initiated by Rockafellar.

AB - The aim of this paper is to show that every representative function of a maximally
monotone operator is the Fitzpatrick transform of a bifunction corresponding
to the operator. In fact, for each representative function ϕ of the operator, there is a
family of equivalent saddle functions (i.e., bifunctions which are concave in the first
and convex in the second argument) each of which has ϕ as Fitzpatrick transform.
In the special case where ϕ is the Fitzpatrick function of the operator, the family of
equivalent saddle functions is explicitly constructed. In thiswaywe exhibit the relation
between the recent theory of representative functions, and the much older theory of
saddle functions initiated by Rockafellar.

KW - Fitzpatrick function

KW - Fitzpatrick transform

KW - Maximal monotonicity

KW - representative function

KW - Fitzpatrick function

KW - Fitzpatrick transform

KW - Maximal monotonicity

KW - representative function

UR - http://hdl.handle.net/10807/78681

U2 - 10.1007/s10107-016-1020-8

DO - 10.1007/s10107-016-1020-8

M3 - Article

SN - 0025-5610

VL - 168

SP - 433

EP - 448

JO - Mathematical Programming

JF - Mathematical Programming

ER -