Description: |
Levenberg-Marquardt algorithm for multivariate optimization.
The Levenberg-Marquardt Method is recommended, if such a function as F = f1 2(x1 ,...,xn ) + ... + fm 2(x1 ,...,xn ) needs to be minimized. The algorithm combines advantages of the steepest descent method (that is, minimization along the direction of the gradient) with the Newton method (that is, using a quadratic model to speed up the process of finding the minimum of a function). This algorithm obtained its operating stability from the steepest descent method, and adopted its accelerated convergence in the minimum vicinity from the Newton method. Standard implementation of the Levenberg-Marquardt algorithm (LMA), its drawbacks, and the updated algorithm version in the ALGLIB package are discussed below. The reader is recommended to familiarise himself/herself with the algorithm description on Wikipedia or in Numerical Recipes, prior to studying the following part. It is assumed hereinafter that the reader is familiar with the general principles of operating the Levenberg-Marquardt algorithm. |