TITLE: Curvature of a polytope
ABSTRACT:
Similarly to the diameter of a polytope, one may define its curvature
based
on the worst-case central path associated with solving an LP posed over
the
polytope. Furthermore, a continuous analogue of the Hirsch conjecture
and a
discrete analogue of the "average curvature" result of Dedieu,
Malajovich
and Shub may be introduced. A continuous analogue of the result of Holt
and
Klee --a polytope construction that attains a linear order largest total
curvature-- and a continuous analogue of a d-step equivalence result for
the
diameter of a polytope may also be proved. We survey the recent progress
towards better understanding of the curvature.