A convergent variant of the Nelder-Mead algorithm
Journal of Optimization Theory and Applications
Numerical Optimization for the Location of Wastewater Outfalls
Computational Optimization and Applications
A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise
Computational Optimization and Applications
Grid Restrained Nelder-Mead Algorithm
Computational Optimization and Applications
Disentangling mark/point interaction in marked-point processes
Computational Statistics & Data Analysis
A novel three-phase trajectory informed search methodology for global optimization
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Optimisation of the antenna placement for an airport surveillance system
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Vertical slot fishways: Mathematical modeling and optimal management
Journal of Computational and Applied Mathematics
Sprouting search-an algorithmic framework for asynchronous parallel unconstrained optimization
Optimization Methods & Software
Optimal design and operation of a wastewater purification system
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An application of optimal control theory to river pollution remediation
Applied Numerical Mathematics
A restarted and modified simplex search for unconstrained optimization
Computers and Operations Research
Flow regulation for water quality restoration in a river section: Modeling and control
Journal of Computational and Applied Mathematics
Optimization in Non-Standard Problems. An Application to the Provision of Public Inputs
Computational Economics
A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization
Mathematics and Computers in Simulation
A derivative-free constrained predictive controller
ICS'06 Proceedings of the 10th WSEAS international conference on Systems
A robust memetic algorithm with self-stopping capabilities
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Implementing the Nelder-Mead simplex algorithm with adaptive parameters
Computational Optimization and Applications
A new evolutionary search strategy for global optimization of high-dimensional problems
Information Sciences: an International Journal
A derivative-free approximate gradient sampling algorithm for finite minimax problems
Computational Optimization and Applications
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The Nelder--Mead algorithm can stagnate and converge to a nonoptimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for all iterations, will guarantee convergence of the Nelder--Mead iteration to a stationary point if the objective function is smooth and the diameters of the Nelder--Mead simplices converge to zero. Failure of this condition is an indicator of potential stagnation. As a remedy we propose a new step, which we call an oriented restart, that reinitializes the simplex to a smaller one with orthogonal edges whose orientation is determined by an approximate descent direction from the current best point. We also give results that apply when the objective function is a low-amplitude perturbation of a smooth function. We illustrate our results with some numerical examples.