An efficient method for finding the minimum of a function of several variables without calculating derivatives

1964/02/01 by M. J. D. Powell · 52 citations
Mathematics · Computer Science · #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research

paper · doi:10.1093/comjnl/7.2.155

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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