Parameter Inversion Using Unconstrained Nonlinear Optimization Methods

In this article, we will explore in-depth how to implement parameter inversion using MATLAB through unconstrained nonlinear optimization methods. Specifically, we will demonstrate the implementation of Powell's method optimization subroutine, which serves as an efficient algorithm for unconstrained nonlinear optimization problems. The implementation involves creating a main optimization function that iteratively calls Powell's direction set method to minimize objective functions without requiring derivative information. Additionally, we will examine the MATLAB generalized least squares algorithm program, which can be integrated with optimization routines to handle parameter estimation problems with correlated errors. These algorithms and programs provide practical solutions for solving complex optimization challenges in engineering and scientific applications, enabling researchers to achieve more accurate results through proper parameter tuning and convergence criteria setting.