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Search schemes for random optimization algorithms that preserve the asymptotic distribution

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Chang C. Y. Dorea  and
Cátia R. Gonçalves
Chang C. Y. Dorea*
Affiliation:
Universidade de Brasília
Cátia R. Gonçalves*
Affiliation:
Universidade Estadual Paulista
*
∗Postal address: Departamento de Matemática, Universidade de Brasília, Caixa Postal 04322, 70910–900 Brasília, Brasil. Email address: cdorea@mat.unb.br
∗∗Postal address: Departmento de Matemática, Universidade Estadual Paulista, 19060–900 Presdidente Prudente, Saō Paulo, Brasil. Research partially supported by CNPq-Brazil.
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Abstract

Markovian algorithms for estimating the global maximum or minimum of real valued functions defined on some domain Ω ⊂ ℝd are presented. Conditions on the search schemes that preserve the asymptotic distribution are derived. Global and local search schemes satisfying these conditions are analysed and shown to yield sharper confidence intervals when compared to the i.i.d. case.

Keywords

Random search algorithmsglobal optimizationsearch schemesasymptotic distribution

MSC classification

Primary: 65K99: None of the above, but in this section 60G70: Extreme value theory; extremal processes
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 825 - 836
Copyright
Copyright © Applied Probability Trust 1999 

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