Global optimization of bilinear programs with a multiparametric disaggregation technique

Abstract

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scale much more favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smaller mixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.

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Acknowledgments

Ignacio Grossmann and Scott Kolodziej acknowledge financial support from the National Science Foundation under Grant OCI-0750826. Pedro Castro gratefully acknowledges financial support from the Luso-American Foundation, under the 2011 Portugal-U.S. Research Networks Program.

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Correspondence to Ignacio E. Grossmann.

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Kolodziej, S., Castro, P.M. & Grossmann, I.E. Global optimization of bilinear programs with a multiparametric disaggregation technique. J Glob Optim 57, 1039–1063 (2013). https://doi.org/10.1007/s10898-012-0022-1

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Keywords

  • Global optimization
  • Mixed integer linear programming
  • Mixed integer nonlinear programming
  • Quadratic optimization
  • Disjunctive programming