TY - JOUR
T1 - A simultaneous lifting strategy for identifying new classes of facets for the Boolean quadric polytope
AU - Sherali, Hanif D.
AU - Lee, Youngho
AU - Adams, Warren P.
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. DMII-9121419, and by the Air Force Office of ScientificR esearchu nderGrant No. AFOSR-90-0191.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1995/2
Y1 - 1995/2
N2 - We develop a framework for characterizing classes of facets for the Boolean quadric polytope obtainable through a simultaneous lifting procedure. In particular, we begin with a class of product-form facets that subsume Padberg's clique, cut, and generalized cut inequality facets. By applying the proposed general approach to this class of facets, we derive a specially structured polyhedron whose vertices describe all facets that are simultaneous liftings of these facets. We identify specific classes of vertices for this polyhedron to reveal a new class of facets for the quadric polytope. Such an approach can be applied to lifting other facets, as well as to analyze other combinatorial optimization problems.
AB - We develop a framework for characterizing classes of facets for the Boolean quadric polytope obtainable through a simultaneous lifting procedure. In particular, we begin with a class of product-form facets that subsume Padberg's clique, cut, and generalized cut inequality facets. By applying the proposed general approach to this class of facets, we derive a specially structured polyhedron whose vertices describe all facets that are simultaneous liftings of these facets. We identify specific classes of vertices for this polyhedron to reveal a new class of facets for the quadric polytope. Such an approach can be applied to lifting other facets, as well as to analyze other combinatorial optimization problems.
KW - Cut polytope
KW - Facets
KW - Lifting
KW - Quadric polytope
KW - Reformulation-linearization-technique
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U2 - 10.1016/0167-6377(94)00065-E
DO - 10.1016/0167-6377(94)00065-E
M3 - Article
AN - SCOPUS:0029254543
VL - 17
SP - 19
EP - 26
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 1
ER -