An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives

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.

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.

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