Optimization and Engineering

, Volume 3, Issue 3, pp 281–303 | Cite as

Product Disaggregation in Global Optimization and Relaxations of Rational Programs

  • Mohit Tawarmalani
  • Shabbir Ahmed
  • Nikolaos V. Sahinidis


We consider the product of a single continuous variable and the sum of a number of continuous variables. We show that “product disaggregation” (distributing the product over the sum) leads to tighter linear programming relaxations, much like variable disaggregation does in mixed-integer linear programming. We also derive closed-form expressions characterizing the exact region over which these relaxations improve when the bounds of participating variables are reduced.

In a concrete application of product disaggregation, we develop and analyze linear programming relaxations of rational programs. In the process of doing so, we prove that the task of bounding general linear fractional functions of 0–1 variables is \(\mathcal{N}\mathcal{P}\)-hard. Finally, we present computational experience to demonstrate that product disaggregation is a useful reformulation technique for global optimization problems.

global optimization relaxation gap convex extensions range reduction 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Mohit Tawarmalani
    • 1
  • Shabbir Ahmed
    • 2
  • Nikolaos V. Sahinidis
    • 3
  1. 1.Krannert School of ManagementPurdue UniversityWest Lafayette
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlanta
  3. 3.Department of Chemical and Biomolecular EngineeringUniversity of Illinois at Urbana-ChampaignUrbana

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