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A hyperbolic variant of the Nelder-Mead simplex method in low dimensions. (English) Zbl 1296.65090

Summary: The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically proven convergence properties. The original formulation of the algorithm is stated in \(\mathbb R^{n}\) using terms of Euclidean geometry. In this paper we introduce the idea of a hyperbolic variant of this algorithm using the Poincaré disk model of the Bolyai-Lobachevsky geometry. We present a few basic properties of this method and we also give a Matlab implementation in 2 and 3 dimensions

MSC:

65K05 Numerical mathematical programming methods
51M10 Hyperbolic and elliptic geometries (general) and generalizations
30F45 Conformal metrics (hyperbolic, Poincaré, distance functions)
90C30 Nonlinear programming

Software:

Matlab
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Full Text: DOI

References:

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