engleski

Efficient Termination Test for the Nelder-Mead Search Algorithm

Nelder--Mead or simplex search algorithm is one of the best known algorithms for unconstrained optimization of non--smooth functions. A fairly simple efficiency analysis of each iteration step reveals a potential computational bottleneck in the domain convergence test. To be efficient, such a test has to be sublinear in the number of vertices of the working simplex. We have tested some of the most common implementations of the Nelder--Mead algorithm, and none of them is efficient in this sense. Therefore, we propose a simple and efficient domain convergence test and discuss some of its properties. This test is based on tracking the volume of the working simplex throughout the iterations.

Nelder-Mead search algorithm; efficient implementation

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