A Stochastic Convergence Result for the Nelder–Mead Simplex Method

Aurél Galántai

doi:10.3390/math11091998

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A Stochastic Convergence Result for the Nelder–Mead Simplex Method

Aurél Galántai

Year: 2023 Journal: Mathematics Vol: 11 (9)Pages: 1998-1998 Publisher: Multidisciplinary Digital Publishing Institute

DOI: 10.3390/math11091998

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Abstract

We prove that the Nelder–Mead simplex method converges in the sense that the simplex vertices converge to a common limit point with a probability of one. The result may explain the practical usefulness of the Nelder–Mead method.

Keywords:

Simplex Convergence (economics) Simplex algorithm Limit (mathematics) Mathematical optimization Mathematics Point (geometry) Computer science Applied mathematics Linear programming Combinatorics Mathematical analysis Economics

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Advanced Optimization Algorithms Research

Physical Sciences → Mathematics → Numerical Analysis

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Stochastic Gradient Optimization Techniques

Physical Sciences → Computer Science → Artificial Intelligence

A Stochastic Convergence Result for the Nelder–Mead Simplex Method

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