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 in [SIAM J. Optim. 21(3) (2011), pp. 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.
|Place of Publication||Ithaca|
|Publisher||Cornell University Library|
|Number of pages||12|
|Publication status||Published - Mar 2017|
- polynomial optimization
- semidefinite optimization
- Lasserre hierarchy
- simulated annealing
de Klerk, E., & Laurent, M. (2017). Comparison of Lasserre's Measure-based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing. (arXiv; Vol. 1703.00744). Cornell University Library.