TY - JOUR
T1 - New properties of the Variational Sum of monotone operators
AU - Ramos, Yboon García
PY - 2009/12/1
Y1 - 2009/12/1
N2 - We study the Variational Sum of monotone operators, in particular its relationship with the Extended Sum of monotone operators. First, we establish some new properties of the Variational Sum, among them that this sum has closed graph and convex values. Then, we show that the graph of the Variational Sum always contains the graph of the Extended Sum, and hence, it contains also the graph of the usual sum. An example is given showing that the latter inclusions are proper in general.
AB - We study the Variational Sum of monotone operators, in particular its relationship with the Extended Sum of monotone operators. First, we establish some new properties of the Variational Sum, among them that this sum has closed graph and convex values. Then, we show that the graph of the Variational Sum always contains the graph of the Extended Sum, and hence, it contains also the graph of the usual sum. An example is given showing that the latter inclusions are proper in general.
KW - Extended sum
KW - Monotone operator
KW - Variational Sum
KW - Extended sum
KW - Monotone operator
KW - Variational Sum
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M3 - Article in a journal
SN - 0944-6532
VL - 16
SP - 767
EP - 778
JO - Journal of Convex Analysis
JF - Journal of Convex Analysis
IS - 3-4
ER -