Convex sets

Saturday, January 20, 2007 - 2:30pm - 3:20pm
Jean Lasserre (Centre National de la Recherche Scientifique (CNRS))
We provide a sufficient condition on a class of
compact basic semialgebraic sets K for their convex hull
to have a lifted semidefinite representation (SDr). This lifted
is explicitly expressed in terms of the polynomials that define
Examples are provided. For convex and compact basic
semi-algebraic sets
K defined by concave polynomials,
we also provide an explicit lifted SDr when the nonnegative
Lf associated with
K and any linear polynomial f, is a sum of squares. We then
Friday, January 19, 2007 - 2:30pm - 3:20pm
Victor Vinnikov (Ben Gurion University of the Negev)
I will discuss the characterization of convex sets in m
which can be represented by Linear Matrix Inequalities, i.e., as feasible
sets of semidefinite programmes. There is a simple necessary condition,
called rigid convexity, which has been shown to be sufficient for sets in
the plane and is conjectured to be sufficient (in a somewhat weakened
sense) for any m.

This should be contrasted with the situation for matrix convex sets that
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