Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Taxonomy of Global Optimization Methods Based on Response Surfaces
Journal of Global Optimization
Computer experiments and global optimization
Computer experiments and global optimization
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Simulated annealing in the presence of noise
Journal of Heuristics
An adaptive multidimensional version of the Kiefer-Wolfowitz stochastic approximation algorithm
Winter Simulation Conference
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We consider the problem of the global minimization of a function observed with noise. This problem occurs for example when the objective function is estimated through stochastic simulations. We propose an original method for iteratively partitioning the search domain when this area is a finite union of simplexes. On each subdomain of the partition, we compute an indicator measuring if the subdomain is likely or not to contain a global minimizer. Next areas to be explored are chosen in accordance with this indicator. Confidence sets for minimizers are given. Numerical applications show empirical convergence results, and illustrate the compromise to be made between the global exploration of the search domain and the focalization around potential minimizers of the problem.