Comparison of Lasserre's measure-based bounds for polynomial optimization to bounds obtained by simulated annealing

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Abstract

We consider the problem of minimizing a continuous function f over a compact set K. We compare the hierarchy of upper bounds proposed by Lasserre [Lasserre JB (2011) A new look at nonnegativity on closed sets and polynomial optimization. SIAM J. Optim. 21(3):864–885] to bounds that may be obtained from simulated annealing. We show that, when f is a polynomial and K a convex body, this comparison yields a faster rate of convergence of the Lasserre hierarchy than what was previously known in the literature.
Original languageEnglish
Pages (from-to)1317-1325
JournalMathematics of Operations Research
Volume43
Issue number4
DOIs
Publication statusPublished - Nov 2018

Keywords

  • polynomial optimization
  • semidefinite optimization
  • Lasserre hierarchy
  • simulated annealing

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