Bound-Constrained Polynomial Optimization Using Only Elementary Calculations

@article{Klerk2017BoundConstrainedPO,
  title={Bound-Constrained Polynomial Optimization Using Only Elementary Calculations},
  author={Etienne de Klerk and Jean Bernard Lasserre and Monique Laurent and Zhao Sun},
  journal={Math. Oper. Res.},
  year={2017},
  volume={42},
  pages={834-853}
}
We provide a monotone nonincreasing sequence of upper bounds fkH(k≥1) converging to the global minimum of a polynomial f on simple sets like the unit hypercube in ℝn. The novelty with respect to the converging sequence of upper bounds in Lasserre [Lasserre JB (2010) A new look at nonnegativity on closed sets and polynomial optimization, SIAM J. Optim. 21:864–885] is that only elementary computations are required. For optimization over the hypercube [0, 1]n, we show that the new bounds fkH have… 

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