Jesus A. De Loera
Not all simplicial polytopes are weakly vertex-decomposable.
Fri, 03/09/2012 - 15:01 — SomNambulAuthors: Jesus A. De Loera, Steven Klee
Subjects: Combinatorics
AbstractIn 1980 Provan and Billera defined the notion of weak $k$-decomposability for
pure simplicial complexes. They showed the diameter of a weakly
$k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial
function of the number of $k$-faces in $\Delta$ and its dimension. For weakly
0-decomposable complexes, this bound is linear in the number of vertices and
the dimension. In this paper we exhibit the first examples of non-weakly
0-decomposable simplicial polytopes.Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Jesus A. De Loera, Peter N. Malkin, Pablo A. Parrilo
Subjects: Optimization and Control
AbstractThe purpose of this note is to survey a methodology to solve systems of
polynomial equations and inequalities. The techniques we discuss use the
algebra of multivariate polynomials with coefficients over a field to create
large-scale linear algebra or semidefinite programming relaxations of many
kinds of feasibility or optimization questions. We are particularly interested
in problems arising in combinatorial optimization.
User login
