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SUMMARY:Algebraic and Geometric Ideas in Discrete Optimisation III - De Lo
 era\, J (University of California\, Davis)
DTSTART:20130715T150000Z
DTEND:20130715T160000Z
UID:TALK46222@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:It is common knowledge that the understanding of the combinato
 rial geometry of convex bodies has helped speed up algorithms in discrete 
 optimization. For example\, cutting planes and facet-description of polyhe
 dra have been crucial in the success of branch-and-bound algorithms for mi
 xed integer linear programming. Another example\, is how the ellipsoid met
 hod can be used to prove polynomiality results in combinatorial optimizati
 on. For the future\, the importance of algebraic-combinatorial geometry in
  optimization appears even greater. \n\nIn the past 5 years advances in al
 gebraic-geometric algorithms have been used to prove unexpected new result
 s on the computation of non-linear integer programs. These lectures will i
 ntroduce the audience to new techniques. I will describe several algorithm
 s and explain why we can now prove theorems that were beyond our reach bef
 ore\, mostly about integer optimization with non-linear objectives. I will
  also describe attempts to turn these two algorithms into practical comput
 ation\, not just in theoretical results. \n\nThis a nice story collecting 
 results by various authors and now contained in our monograph recently pub
 lished by SIAM-MOS.\n
LOCATION:Seminar Room 1\, Newton Institute
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