Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization

  title={Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization},
  author={Etienne de Klerk and Monique Laurent and Zhao Sun},
  journal={Mathematical Programming},
We consider the problem of minimizing a continuous function f over a compact set $${\mathbf {K}}$$K. We analyze a hierarchy of upper bounds proposed by Lasserre (SIAM J Optim 21(3):864–885, 2011), obtained by searching for an optimal probability density function h on $${\mathbf {K}}$$K which is a sum of squares of polynomials, so that the expectation $$\int _{{\mathbf {K}}} f(x)h(x)dx$$∫Kf(x)h(x)dx is minimized. We show that the rate of convergence is no worse than $$O(1/\sqrt{r})$$O(1/r… 
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