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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Algebraic and Geometric Ideas in Discrete Optimisa
tion I - De Loera\, J (University of California\,
Davis)
DTSTART;TZID=Europe/London:20130715T140000
DTEND;TZID=Europe/London:20130715T144500
UID:TALK46227AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/46227
DESCRIPTION:It is common knowledge that the understanding of t
he combinatorial geometry of convex bodies has hel
ped speed up algorithms in discrete optimization.
For example\, cutting planes and facet-description
of polyhedra have been crucial in the success of
branch-and-bound algorithms for mixed integer line
ar programming. Another example\, is how the ellip
soid method can be used to prove polynomiality res
ults in combinatorial optimization. For the future
\, the importance of algebraic-combinatorial geome
try in optimization appears even greater. \n\nIn t
he past 5 years advances in algebraic-geometric al
gorithms have been used to prove unexpected new re
sults on the computation of non-linear integer pro
grams. These lectures will introduce the audience
to new techniques. I will describe several algorit
hms and explain why we can now prove theorems that
were beyond our reach before\, mostly about integ
er optimization with non-linear objectives. I will
also describe attempts to turn these two algorith
ms into practical computation\, not just in theore
tical results. \n\nThis a nice story collecting re
sults by various authors and now contained in our
monograph recently published by SIAM-MOS.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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