A Stochastic Convergence Result for the Nelder–Mead Simplex Method
Aurél Galántai
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.
Topics & Concepts
SimplexConvergence (economics)Simplex algorithmLimit (mathematics)Mathematical optimizationMathematicsPoint (geometry)Computer scienceApplied mathematicsLinear programmingCombinatoricsMathematical analysisEconomicsEconomic growthGeometryAdvanced Optimization Algorithms ResearchMetaheuristic Optimization Algorithms ResearchStochastic Gradient Optimization Techniques