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Etienne de Klerk (E.deKlerkuvt.nl) Abstract: We provide a monotone non increasing sequence of upper bounds $f^H_k$ ($k\ge 1$) converging to the global minimum of a polynomial $f$ on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper bounds in [J.B. Lasserre, A new look at nonnegativity on closed sets and polynomial optimization, SIAM J. Optim. 21, pp. 864885, 2010] is that only elementary computations are required. For optimization over the hypercube, we show that the new bounds $f^H_k$ have a rate of convergence in $O(1/\sqrt {k})$. Moreover we show a stronger convergence rate in $O(1/k)$ for quadratic polynomials and more generally for polynomials having a rational minimizer in the hypercube. In comparison, evaluation of all rational grid points with denominator $k$ produces bounds with a rate of convergence in $O(1/k^2)$, but at the cost of $O(k^n)$ function evaluations, while the new bound $f^H_k$ needs only $O(n^k)$ elementary calculations. Keywords: Polynomial optimization, boundconstrained optimization, Lasserre hierarchy Category 1: Nonlinear Optimization (Boundconstrained Optimization ) Category 2: Global Optimization (Theory ) Citation: Technical report, Tilburg University, CWI Amsterdam and LAASCNRS, July 2015. Download: [PDF] Entry Submitted: 07/15/2015 Modify/Update this entry  
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