MATLAB Implementation Example of DFP Algorithm with Source Code

In this article, we will demonstrate how to implement the DFP algorithm using MATLAB and provide a detailed source code example. The DFP algorithm is an optimization method designed for solving unconstrained optimization problems. It employs an iterative approach known as the quasi-Newton method, which approximates solutions by estimating the inverse of the Hessian matrix of the objective function. The implementation will include key components such as: - Initialization of the inverse Hessian approximation matrix - Gradient calculation using finite differences or symbolic differentiation - Line search implementation for step size determination - Matrix update rules following the DFP formula We will explain the algorithm's background and theoretical principles, along with practical implementation techniques in MATLAB. The provided source code will allow you to experiment with the DFP algorithm, modify its parameters, and optimize its performance for specific applications. This example covers error handling, convergence criteria, and visualization of optimization progress. This article aims to deepen your understanding of optimization algorithms and enhance your ability to apply them effectively in practical scenarios. The code includes comments explaining each major section and suggestions for potential improvements.