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DAGSTUHL
2004

Optimal algorithms for global optimization in case of unknown Lipschitz constant

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Optimal algorithms for global optimization in case of unknown Lipschitz constant
We consider the global optimization problem for d-variate Lipschitz functions which, in a certain sense, do not increase too slowly in a neighborhood of the global minimizer(s). On these functions, we apply optimization algorithms which use only function values. We propose two adaptive deterministic methods. The first one applies in a situation when the Lipschitz constant L is known. The second one applies if L is unknown. We show that for an optimal method, adaptiveness is necessary and that randomization (Monte-Carlo) yields no further advantage. Both algorithms presented have the optimal rate of convergence. Key words: Global optimization, Lipschitz functions, complexity, optimal rate of convergence MSC: primary 90C60, 90C56; secondary 68Q25, 26B35
Matthias U. Horn
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2004
Where DAGSTUHL
Authors Matthias U. Horn
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