Canonical Dual Solutions for Fixed Cost Quadratic Programs

  • David Yang GaoEmail author
  • Ning Ruan
  • Hanif D. Sherali
Part of the Springer Optimization and Its Applications book series (SOIA, volume 39)


This chapter presents a canonical dual approach for solving a mixed-integer quadratic minimization problem with fixed cost terms. We show that this well-known NP-hard problem in \(\mathbb{R}^{2n}\) can be transformed into a continuous concave maximization dual problem over a convex feasible subset of \(\mathbb{R}^{2n}\) with zero duality gap. The resulting canonical dual problem can be solved easily, under certain conditions, by traditional convex programming methods. Both existence and uniqueness of global optimal solutions are discussed. Application to a decoupled mixed-integer problem is illustrated and analytic solutions for both a global minimizer and a global maximizer are obtained. Examples for both decoupled and general nonconvex problems are presented. Furthermore, we discuss connections between the proposed canonical duality theory approach and the classical Lagrangian duality approach. An open problem is proposed for future study.


canonical duality Lagrangian duality global optimization mixed-integer programming fixed-charge objective function 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Graduate School of Information Technology and Mathematical SciencesUniversity of BallaratMt HelenAustralia
  2. 2.Grado Department of Industrial and Systems EngineeringVirginia TechBlacksburgUSA

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