Compact relaxations for polynomial programming problems

Authors:
Sonia Cafieri;Pierre Hansen;Lucas Létocart;Leo Liberti;Frédéric Messine
Affiliations:
Laboratoire MAIAA, Ecole Nationale de l'Aviation Civile, Toulouse, France;GERAD, HEC Montreal, Canada,LIX, École Polytechnique, Palaiseau, France;LIPN, Univ. de Paris Nord, Villetaneuse, France;LIX, École Polytechnique, Palaiseau, France;ENSEEIHT-IRIT, Toulouse, France
Venue:
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Year:
2012

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Abstract

Reduced RLT constraints are a special class of Reformulation-Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach.