Lov^sz and Schrijver (1991) described a semidcfinile operator for generating strong valid inequalities for the 0-! vectors in a prescribed polyhedron. Among their resuli.s. they showed ihai ii iterations of the operator are .sufficient to generate the convex hull ot" O-l vectors contained in a polyhedron in /i-space. We give a simple example, having Chvdtal rank 1. tliat meetii this worst case bound of ;i. We describe another example requiring « iterations even when combinini; ihe scniidefinite and Gomory-Chviltal operators. Thi.s second example is used to show ihai the standard linear programming relaxation of a A-city traveling salesman problem requires at least [k/^l iterations of the combined operaior; Lhis bound is best possible, up to a consiani factor, as A HI iterations suffice.
[1]
C. Burdet,et al.
On cutting planes
,
1973
.
[2]
Tamon Stephen,et al.
On a Representation of the Matching Polytope Via Semidefinite Liftings
,
1999,
Math. Oper. Res..
[3]
László Lovász,et al.
Critical Facets of the Stable Set Polytope
,
2001,
Comb..
[4]
Gregory Gutin,et al.
The traveling salesman problem
,
2006,
Discret. Optim..
[5]
Alexander Schrijver,et al.
Cones of Matrices and Set-Functions and 0-1 Optimization
,
1991,
SIAM J. Optim..
[6]
Friedrich Eisenbrand,et al.
On the Chvátal Rank of Polytopes in the 0/1 Cube
,
1999,
Discret. Appl. Math..