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

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=73349126402&origin=inward

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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 -