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Completely positive reformulations of polynomial optimization problems with linear constraints

Optimization Letters volume 11, pages 1229–1241 (2017)Cite this article

Abstract

A polynomial optimization problem (POP) is an optimization problem in which both the objective and constraints can be written in terms of polynomials on the decision variables. Recently, it has been shown that under appropriate assumptions POPs can be reformulated as conic problems over the cone of completely positive tensors; which generalize the set of completely positive matrices. Here, we show that by explicitly handling the linear constraints in the formulation of the POP, one obtains a generalization of the completely positive reformulation of quadratically constrained quadratic programs recently introduced by Bai et al. (Math Program 1–28, 2016).

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Acknowledgements

We would like to thank an anonymous referee for providing thoughtful and thorough comments to improve the article. The work of Wei Xia and Luis F. Zuluaga are supported by NSF Grant CMMI-1300193.

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Authors and Affiliations

  1. Industrial and System Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015, USA

    Wei Xia & Luis F. Zuluaga

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  1. Wei Xia
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  2. Luis F. Zuluaga
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Correspondence to Wei Xia.

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Xia, W., Zuluaga, L.F. Completely positive reformulations of polynomial optimization problems with linear constraints. Optim Lett 11, 1229–1241 (2017). https://doi.org/10.1007/s11590-017-1123-z

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  • DOI: https://doi.org/10.1007/s11590-017-1123-z

Keywords

  • Polynomial optimization
  • Completely positive tensors
  • Completely positive relaxations