Optimization Letters

, Volume 11, Issue 7, pp 1229–1241 | Cite as

Completely positive reformulations of polynomial optimization problems with linear constraints

  • Wei XiaEmail author
  • Luis F. Zuluaga
Original Paper


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).


Polynomial optimization Completely positive tensors Completely positive relaxations 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Industrial and System EngineeringLehigh UniversityBethlehemUSA

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