Convexification of bilinear forms through non-symmetric lifting

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.

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Acknowledgements

The authors are grateful to the anonymous referees for making several points which significantly improved the presentation.

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Correspondence to Jon Lee.

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M. Fampa was supported in part by CNPq Grant 303898/2016-0. J. Lee was supported in part by ONR Grant N00014-17-1-2296. Additionally, part of this work was done while J. Lee was visiting the Simons Institute for the Theory of Computing. It was partially supported by the DIMACS/Simons Collaboration on Bridging Continuous and Discrete Optimization through NSF Grant #CCF-1740425.

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Fampa, M., Lee, J. Convexification of bilinear forms through non-symmetric lifting. J Glob Optim (2021). https://doi.org/10.1007/s10898-020-00975-z

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Keywords

  • Global optimization
  • Quadratic
  • Bilinear
  • Mixing