A class of algorithms for computing the minimal value of a convex function f over[0 1] <sup>k</sup> within accuracy ∈, when the evaluations of f are made within accuracy ∈
Fiala, T.; Sonnevend, G.; Fiala, T.; Department of Numerical Analysis and Computer Sciences, Eötvös Loránd University Budapest; Sonnevend, G.; Department of Numerical Analysis and Computer Sciences, Eötvös Loránd University Budapest
Журнал:
Optimization
Дата:
1986
Аннотация:
In this paper an algorithm is presented for the computation of the minimal value of a convex function f-over the unit cube in R<sup>k</sup> -within prescribed accuracy ε=γε<sub>0γ</sub> when the values of f can be computed within accuracy ∈<sub>0</sub> only. This algorithm is a generalization of the golden section search and allows to choose γ arbitrarily near to one; its requirements for memory (working space) and for the number of arithmetical operations (per one function evaluation) are independent of (k, γf).
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