TY - JOUR
T1 - Fenchel-Moreau conjugation for lower semi-continuous functions
AU - Cotrina, John
AU - Karas, Elizabeth W.
AU - Ribeiro, Ademir A.
AU - Sosa, Wilfredo
AU - Yuan, Jin Y.
PY - 2011/8/1
Y1 - 2011/8/1
N2 - We introduce a modification of Fenchel's conjugation which is a particular case of Moreau's conjugation. We obtain good properties such as convexity of the conjugate function even though the function is not convex. We also introduce the concept of conjugate dual space as a class of continuous operators, while in the Fenchel conjugation the conjugate dual space is the classical topological dual space. Finally, we present some examples for illustrating the difference between the Fenchel-Moreau conjugation and our modification.
AB - We introduce a modification of Fenchel's conjugation which is a particular case of Moreau's conjugation. We obtain good properties such as convexity of the conjugate function even though the function is not convex. We also introduce the concept of conjugate dual space as a class of continuous operators, while in the Fenchel conjugation the conjugate dual space is the classical topological dual space. Finally, we present some examples for illustrating the difference between the Fenchel-Moreau conjugation and our modification.
KW - Fenchel-Moreau conjugate
KW - convex function
KW - extension of the Fenchel conjugate
KW - lower semi-continuous function
KW - proper function
KW - Fenchel-Moreau conjugate
KW - convex function
KW - extension of the Fenchel conjugate
KW - lower semi-continuous function
KW - proper function
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84858226482&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84858226482&origin=inward
U2 - 10.1080/02331934.2010.507273
DO - 10.1080/02331934.2010.507273
M3 - Article in a journal
SN - 0233-1934
VL - 60
SP - 1045
EP - 1057
JO - Optimization
JF - Optimization
IS - 8-9
ER -