Topics in Lipschitz global optimisation

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Global optimization of Lipschitz functions

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO wh...

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Global Flows for Stochastic Differential Equations without Global Lipschitz Conditions

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Global Optimisation of Molecular Clusters

All results presented here use the scaled Lennard-Jones potential such that the pair well depth and equilibrium distance are both unity V LJ (r) = 1 r 12 − 2 r 6. (1) Thus all energies are given in units of the pair well depth, , and lengths are given in terms of the equilibrium distance σ. This means that for a dimer the potential and the separation are both one. Clusters of this type exhibit ...

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ژورنال

عنوان ژورنال: Bulletin of the Australian Mathematical Society

سال: 1997

ISSN: 0004-9727,1755-1633

DOI: 10.1017/s0004972700030641