MATLAB Implementation of Conjugate Gradient Method

In this article, we present the Conjugate Gradient Method, which is a well-verified optimization algorithm. While we strongly recommend that readers modify certain parameters when applying this method to other domains, we believe the strength of the Conjugate Gradient Method lies in its flexibility. Through parameter adjustment, the algorithm can adapt to various types of optimization problems and often provides superior results compared to other algorithms in many scenarios. The MATLAB implementation typically involves initializing starting points, setting tolerance thresholds for convergence, and defining maximum iteration limits. Key algorithmic steps include: - Computing the gradient of the objective function - Determining conjugate directions using Fletcher-Reeves or Polak-Ribière formulas - Performing line searches for optimal step sizes - Updating solution vectors iteratively until convergence The code structure usually consists of a main function handling the iterative process, with subfunctions for gradient computation and convergence checking. Important parameters to consider when adapting the implementation include: - Preconditioning matrices for improved convergence - Restart criteria to maintain numerical stability - Tolerance levels for different precision requirements Therefore, we encourage readers to deeply study the Conjugate Gradient Method to better apply this algorithm for solving practical problems, paying particular attention to parameter tuning and problem-specific adaptations in the code implementation.