A simultaneous lifting strategy for identifying new classes of facets for the Boolean quadric polytope

Authors:
Hanif D. Sherali;Youngho Lee;Warren P. Adams
Affiliations:
Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0118, USA;US West Advanced Technologies, 4001 Discovery Drive, Boulder, CO 80303, USA;Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-1907, USA
Venue:
Operations Research Letters
Year:
1995

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Abstract

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.