Abstract:
Co
ncave functions play a central role in optimization theory. So-called
ex-ponentially concave functions are of similar importance in
informat
ion the-ory. In the presentation\, we discuss mathematical
properties
of the class of exponentiallyconcave functions\, like
closedness under
linear and convex combinationand relations to quasi-\,
Jensen- and Sc
hur-concavity. Infor-mationtheoretic quantities such as
self-informati
on and (scaled)entropy are shown to be exponentially
concave. Furtherm
ore\, newinequalities for the Kullback-Leibler
divergence\, for the en
tropyof mixture distributi-ons\,and for mutual
information are present
ed.
Bio:
Gholamreza ALIREZAEI received the Diploma and Doctoral
degree in
electrical engineering from RWTH Aachen University. From 200
2 to 2008\,
he was a research assistant at the Institute of High Frequ
ency
Technology of the Faculty of Electrical Engineering and Informati
on
Technology at RWTH. From 2008 to 2011\, he was the R[&\;]D leade
r at the
ATecoM GmbH. From 2011 onwards\, he is with the Institute for
Theoretical
Information Technology at RWTH and he currently works as
chief engineer
responsible for research\, project acquisition and proj
ect management. In
addition\, he holds lecturer positions with Technic
al University of
Munich (TUM) and RWTH. His research interests include
the design of
communication sys-tems and their development. Furthermo
re\, he tackles
hard mathematical problems arisen from estimation\, cl
assification and
information theory. In particular\, nonconvex optimiz
ation problems\,
analytical resource allocati-on\, signal and target c
lassification\, and
determination of theoretical bounds and inequaliti
es for special
functions have been the main topics in the more recent
past. Gholamreza
has received a number of awards and recognitions. Amo
ng others\, he is
holder of the prestigious Vodafone Y-oung-Researcher
Prize\, the
ITG-Literature Award\, and the Friedrich-Wilhelm Prize. H
e has served as
reviewer and member of the Technical Program Committee
in numerous IEEE
conferences\, including ICC\, ISIT\, ISWCS\, GLOBECO
M and WiSEE. He also
serves as reviewer for both the IEEE Transactions
on Signal Processing
and the IEEE Transactions on Wireless Communicat
ions.