MATLAB Implementation of Conjugate Gradient Method

In this article, we present a MATLAB implementation of the conjugate gradient method to help you find extrema of nonlinear or linear equations. First, let's explore the conjugate gradient method in greater detail. This numerical optimization technique is designed to locate minima or maxima of objective functions. The algorithm combines advantages of both conjugate gradient and gradient descent methods, providing efficient solutions for nonlinear problems. When implementing this method, you need to supply initial points and the gradient of the objective function. Our MATLAB implementation includes key components such as gradient calculation, direction vector updates using conjugate directions, and step size optimization through line search techniques. The code structure features main functions for iteration control, convergence checking with tolerance settings, and gradient computation handling. We provide complete MATLAB source code to facilitate straightforward implementation of the conjugate gradient method, including comments explaining algorithmic steps and parameter configurations. This article aims to enhance your understanding of the conjugate gradient method and demonstrate its practical application in MATLAB for finding equation extrema through optimized code implementation.