Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization

Naohiko Arima, Sunyoung Kim, Masakazu Kojima

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Abstract

We propose the moment cone relaxation for a class of polynomial optimization problems to extend the results on the completely positive cone programming relaxation for the quadratic optimization model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the polynomial optimization problems, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the polynomial optimization problem and that of the moment cone relaxation under conditions similar to the ones assumed in the quadratic optimization model.

Original languageEnglish
Pages (from-to)884-900
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume168
Issue number3
DOIs
StatePublished - 1 Mar 2016

Keywords

  • Completely positive programming
  • Copositive programming
  • Moment cone relaxation
  • Polynomial optimization

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