Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Frame based methods for unconstrained optimization
Journal of Optimization Theory and Applications
Direct search methods: then and now
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
On the Convergence of Grid-Based Methods for Unconstrained Optimization
SIAM Journal on Optimization
On the Convergence of Pattern Search Algorithms
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
Fortified-Descent Simplicial Search Method: A General Approach
SIAM Journal on Optimization
A convergent variant of the Nelder-Mead algorithm
Journal of Optimization Theory and Applications
RANK ORDERING AND POSITIVE BASES IN PATTERN SEARCH ALGORITHMS
RANK ORDERING AND POSITIVE BASES IN PATTERN SEARCH ALGORITHMS
Multidirectional search: a direct search algorithm for parallel machines
Multidirectional search: a direct search algorithm for parallel machines
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
Optimization in Non-Standard Problems. An Application to the Provision of Public Inputs
Computational Economics
A simplex-based numerical framework for simple and efficient robust design optimization
Computational Optimization and Applications
CARTopt: a random search method for nonsmooth unconstrained optimization
Computational Optimization and Applications
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Probably the most popular algorithm for unconstrained minimization for problems of moderate dimension is the Nelder-Mead algorithm published in 1965. Despite its age only limited convergence results exist. Several counterexamples can be found in the literature for which the algorithm performs badly or even fails. A convergent variant derived from the original Nelder-Mead algorithm is presented. The proposed algorithm's convergence is based on the principle of grid restrainment and therefore does not require sufficient descent as the recent convergent variant proposed by Price, Coope, and Byatt. Convergence properties of the proposed grid-restrained algorithm are analysed. Results of numerical testing are also included and compared to the results of the algorithm proposed by Price et al. The results clearly demonstrate that the proposed grid-restrained algorithm is an efficient direct search method.