Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Frame based methods for unconstrained optimization
Journal of Optimization Theory and Applications
On the Convergence of Grid-Based Methods for Unconstrained Optimization
SIAM Journal on Optimization
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point
SIAM Journal on Optimization
SIAM Journal on Optimization
Conjugate Grids for Unconstrained Optimisation
Computational Optimization and Applications
Grid Restrained Nelder-Mead Algorithm
Computational Optimization and Applications
Sprouting search-an algorithmic framework for asynchronous parallel unconstrained optimization
Optimization Methods & Software
Unconstrained derivative-free optimization by successive approximation
Journal of Computational and Applied Mathematics
A restarted and modified simplex search for unconstrained optimization
Computers and Operations Research
An inexact modified subgradient algorithm for nonconvex optimization
Computational Optimization and Applications
Implementing the Nelder-Mead simplex algorithm with adaptive parameters
Computational Optimization and Applications
A simplex-based numerical framework for simple and efficient robust design optimization
Computational Optimization and Applications
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The Nelder-Mead algorithm (1965) for unconstrained optimization has been used extensively to solve parameter estimation and other problems. Despite its age, it is still the method of choice for many practitioners in the fields of statistics, engineering, and the physical and medical sciences because it is easy to code and very easy to use. It belongs to a class of methods which do not require derivatives and which are often claimed to be robust for problems with discontinuities or where the function values are noisy. Recently (1998), it has been shown that the method can fail to converge or converge to nonsolutions on certain classes of problems. Only very limited convergence results exist for a restricted class of problems in one or two dimensions. In this paper, a provably convergent variant of the Nelder-Mead simplex method is presented and analyzed. Numerical results are included to show that the modified algorithm is effective in practice.