MATLAB Program for Nonlinear Least Squares Optimization Problems

This document provides a comprehensive guide on implementing nonlinear least squares optimization problems using MATLAB to solve various practical applications. We begin by discussing the mathematical formulation of nonlinear least squares problems and their real-world application scenarios. The implementation approach utilizes MATLAB's Optimization Toolbox, focusing on key functions like lsqnonlin for solving nonlinear least-squares problems. We explain the algorithm structure involving objective function definition, where users need to implement a function that returns the residual vector. The programming concepts cover essential MATLAB features including matrix operations for efficient computation and function handle definitions for optimization setup. The document demonstrates practical problem-solving through complete code examples showing parameter initialization, optimization options configuration, and result interpretation. Implementation tips include Jacobian pattern specification for large-scale problems and algorithm selection between trust-region-reflective and Levenberg-Marquardt methods based on problem characteristics. Through this guide, you will gain deeper understanding of nonlinear least squares optimization, master MATLAB programming techniques, and apply these skills effectively in practical engineering and research projects.