`` Direct Search'' Solution of Numerical and Statistical Problems
Journal of the ACM (JACM)
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
A convergent variant of the Nelder-Mead algorithm
Journal of Optimization Theory and Applications
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
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
Frames and Grids in Unconstrained and Linearly Constrained Optimization: A Nonsmooth Approach
SIAM Journal on Optimization
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Grid Restrained Nelder-Mead Algorithm
Computational Optimization and Applications
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We present an algorithmic framework for unconstrained derivative-free optimization based on dividing the search space in regions (partitions). Every partition is assigned a representative point. The representative points form a grid. A piecewise-constant approximation to the function subject to optimization is constructed using a partitioning and its corresponding grid. The convergence of the framework to a stationary point of a continuously differentiable function is guaranteed under mild assumptions. The proposed framework is appropriate for upgrading heuristics that lack mathematical analysis into algorithms that guarantee convergence to a local minimizer. A convergent variant of the Nelder-Mead algorithm that conforms to the given framework is constructed. The algorithm is compared to two previously published convergent variants of the NM algorithm. The comparison is conducted on the More-Garbow-Hillstrom set of test problems and on four variably-dimensional functions with dimension up to 100. The results of the comparison show that the proposed algorithm outperforms both previously published algorithms.