Mathematical Programming

, Volume 136, Issue 1, pp 155–182 | Cite as

Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations

  • Ruth Misener
  • Christodoulos A. Floudas
Full Length Paper Series B


We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to \({\epsilon}\) -global optimality. The facets of low-dimensional (n ≤ 3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib.

Mathematics Subject Classification

90C26 Global optimization 90C20 Quadratic programming 90C57 Polyhedral combinatorics; branch & bound 


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© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  1. 1.Department of Chemical and Biological EngineeringPrinceton UniversityPrincetonUSA

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