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

Etienne De Klerk(e.deklerk***at***uvt.nl)
Monique Laurent(m.laurent***at***cwi.nl)

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 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.

Keywords: Polynomial optimization; Semidefinite optimization; Lasserre hierarchy; simulated annealing

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Nonlinear Optimization

Category 3: Global Optimization

Citation: Tilburg University, February 28, 2017

Download: [PDF]

Entry Submitted: 03/02/2017
Entry Accepted: 03/02/2017
Entry Last Modified: 03/02/2017

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