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SUMMARY:A new convex reformulation and approximation hierarchy for polynom
 ial optimisation - Dickinson\, PJC (University of Groningen)
DTSTART:20130717T150000Z
DTEND:20130717T153000Z
UID:TALK46258@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk we will look at how any polynomial minimisation p
 roblem with a bounded feasible set can be reformulated into a conic maximi
 sation problem with a single variable. By reformulated we mean that the op
 timal values of these problems are equal. The difficulty of the original p
 roblem goes into a cone of homogeneous polynomials which are nonnegative o
 ver a certain subset of the nonnegative orthant. We shall consider a new h
 ierarchy of inner approximations to this cone. These approximations can be
  used to produce linear optimisation problems\, whose optimal values provi
 de a monotonically increasing sequence of lower bounds to the optimal valu
 e of the original problem. Using a new positivstellensatz\, we shall show 
 that this sequence of lower bounds in fact converges to the optimal value 
 of the original problem.\n
LOCATION:Seminar Room 1\, Newton Institute
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