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Mathematics of Computation

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Adaptive search in quasi-Monte Carlo optimization


Authors: Christian Biester, Peter J. Grabner, Gerhard Larcher and Robert F. Tichy
Journal: Math. Comp. 64 (1995), 807-818
MSC: Primary 65C05; Secondary 65K10
MathSciNet review: 1270614
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Abstract: Motivated by a linear time-complexity result for an adaptive Monte Carlo algorithm, we propose and analyze an adaptive deterministic algorithm. We restrict a grid search to nested subregions that promise to provide improvement of the current solution, and we obtain an exponential rate of convergence in function evaluations. For proving the main result we restrict ourselves to functions on hypercubes. In a final section we outline how to extend the method to the general case and give some numerical examples.


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DOI: https://doi.org/10.1090/S0025-5718-1995-1270614-4
Article copyright: © Copyright 1995 American Mathematical Society