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Convexification of bilinear forms through non-symmetric lifting

Author

Listed:
  • Marcia Fampa

    (Universidade Federal do Rio de Janeiro)

  • Jon Lee

    (University of Michigan)

Abstract

We efficiently treat bilinear forms in the context of global optimization, by applying McCormick convexification and by extending an approach of Saxena et al. (Math Prog Ser B 124(1–2):383–411, 2010) for symmetric quadratic forms to bilinear forms. A key application of our work is in treating “structural convexity” in a symmetric quadratic form.

Suggested Citation

  • Marcia Fampa & Jon Lee, 2021. "Convexification of bilinear forms through non-symmetric lifting," Journal of Global Optimization, Springer, vol. 80(2), pages 287-305, June.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:2:d:10.1007_s10898-020-00975-z
    DOI: 10.1007/s10898-020-00975-z
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    References listed on IDEAS

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    1. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    2. Marcia Fampa & Jon Lee & Wendel Melo, 2017. "On global optimization with indefinite quadratics," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 309-337, September.
    3. Marco Locatelli, 2016. "Polyhedral subdivisions and functional forms for the convex envelopes of bilinear, fractional and other bivariate functions over general polytopes," Journal of Global Optimization, Springer, vol. 66(4), pages 629-668, December.
    4. Wei Xia & Juan C. Vera & Luis F. Zuluaga, 2020. "Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 40-56, January.
    5. Pedro Castro & Ignacio Grossmann, 2014. "Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems," Journal of Global Optimization, Springer, vol. 59(2), pages 277-306, July.
    6. Scott Kolodziej & Pedro Castro & Ignacio Grossmann, 2013. "Global optimization of bilinear programs with a multiparametric disaggregation technique," Journal of Global Optimization, Springer, vol. 57(4), pages 1039-1063, December.
    Full references (including those not matched with items on IDEAS)

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