A Reformulation-Linearization Technique (RLT) for semi-infinite and convex programs under mixed 0-1 and general discrete restrictions

Authors:
Hanif D. Sherali;Warren P. Adams
Affiliations:
Virginia Polytechnic Institute and State University, Grado Department of Industrial and Systems Engineering (0118), 250 Durham Hall, Blacksburg, VA 24061, United States;Clemson University, Department of Mathematical Sciences, O-327 Martin Hall, Clemson, SC 29634-0975, United States
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The Reformulation-Linearization Technique (RLT) provides a hierarchy of relaxations spanning the spectrum from the continuous relaxation to the convex hull representation for linear 0-1 mixed-integer and general mixed-discrete programs. We show in this paper that this result holds identically for semi-infinite programs of this type. As a consequence, we extend the RLT methodology to describe a construct for generating a hierarchy of relaxations leading to the convex hull representation for bounded 0-1 mixed-integer and general mixed-discrete convex programs, using an equivalent semi-infinite linearized representation for such problems as an intermediate stepping stone in the analysis. For particular use in practice, we provide specialized forms of the resulting first-level RLT formulation for such mixed 0-1 and discrete convex programs, and illustrate these forms through two examples.