Naslov
Complexity Analysis of Nelder--Mead Search Iterations

Autori
Singer, Sanja ; Singer, Saša

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Applied Mathematics and Computation / Rogina, M ; Hari, V ; Limić, N ; Tutek , Z - Zagreb, 2001, 185-196

Skup
Applied Mathematics and Computation

Mjesto i datum
Dubrovnik, Hrvatska, 13.09.1999. - 18.09.1999

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
optimization; direct search methods; Nelder--Mead simplex algorithm;complexity; termination criteria

Sažetak
A random field on a bounded domain is usually estimated from data by using the linear least square estimation. To apply this method it is necessary to know the covariance function, while distribution of field at a point is not used. Better results of estimation are expected by applying methods for which the distribution of field must be utilized. We consider here a method We investigate potential computational bottlenecks in the Nelder--Mead search (NMS) algorithm. Many implementations of the algorithm exist, differing mainly in the selection of convergence or termination criteria and some minor computational details. Therefore, a fairly general complexity analysis of a single NMS iteration step is presented, which leads to a simple efficiency measure. Efficiency analysis of the most common NMS implementations clearly identifies a computational bottleneck in domain convergence criterion. This seriously affects the performance of the method, at least for discontinuous functions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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