کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4641691 1341317 2009 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Unconstrained derivative-free optimization by successive approximation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Unconstrained derivative-free optimization by successive approximation
چکیده انگلیسی

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 Moré–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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 223, Issue 1, 1 January 2009, Pages 62–74
نویسندگان
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