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 language | English |
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Pages (from-to) | 1317-1325 |
Journal | Mathematics of Operations Research |
Volume | 43 |
Issue number | 4 |
DOIs | |
Publication status | Published - Nov 2018 |
Keywords
- polynomial optimization
- semidefinite optimization
- Lasserre hierarchy
- simulated annealing