Journal of Global Optimization

, Volume 6, Issue 1, pp 39–76

A global optimization algorithm for linear fractional and bilinear programs

  • Ignacio Quesada
  • Ignacio E. Grossmann

DOI: 10.1007/BF01106605

Cite this article as:
Quesada, I. & Grossmann, I.E. J Glob Optim (1995) 6: 39. doi:10.1007/BF01106605


In this paper a deterministic method is proposed for the global optimization of mathematical programs that involve the sum of linear fractional and/or bilinear terms. Linear and nonlinear convex estimator functions are developed for the linear fractional and bilinear terms. Conditions under which these functions are nonredundant are established. It is shown that additional estimators can be obtained through projections of the feasible region that can also be incorporated in a convex nonlinear underestimator problem for predicting lower bounds for the global optimum. The proposed algorithm consists of a spatial branch and bound search for which several branching rules are discussed. Illustrative examples and computational results are presented to demonstrate the efficiency of the proposed algorithm.

Key words

Nonconvex optimization bilinear programming fractional programming convex under estimators 

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Ignacio Quesada
    • 1
  • Ignacio E. Grossmann
    • 1
  1. 1.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA

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