An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives¶
Authors: M. J. D. Powell
Published: 1964 (Journal Paper)
Source: The Computer Journal
Algorithm: Powell's Method
DOI: 10.1093/comjnl/7.2.155
Summary¶
Introduces Powell's derivative-free conjugate-direction method for unconstrained minimization. The method builds useful search directions from successive one-dimensional minimizations, making it a foundational direct-search optimizer for smooth problems when derivatives are unavailable or inconvenient.
Abstract¶
A simple variation of the well-known method of minimizing a function of several variables by changing one parameter at a time is described. This variation is such that when the procedure is applied to a quadratic form, it causes conjugate directions to be chosen, so the ultimate rate of convergence is fast when the method is used to minimize a general function. A further variation completes the method, and its ensures that the convergence rate from a bad approximation to a minimum is always efficient. Practical applications of the procedure have proved to be very satisfactory, and numerical examples are given in which functions of up to twenty variables are minimized.
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Tags¶
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Derivative-free optimization
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Powell's method
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Conjugate directions
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Unconstrained optimization
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Numerical optimization
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Direct search