Function Optimization Using Wolfe-Powell Criterion with Inexact Line Search Algorithm

This paper presents a simulation process for solving function optimization problems using the Wolfe-Powell criterion combined with an inexact line search method to determine the optimal step size. The Wolfe-Powell criterion serves as an effective nonlinear search technique that enhances algorithm convergence speed during optimization procedures. In our implementation, we carefully coded the two primary conditions of the Wolfe-Powell criterion: the sufficient decrease condition (Armijo condition) and the curvature condition, ensuring proper balance between step size reduction and computational efficiency. The simulation incorporates key algorithmic components including gradient calculation functions, objective function evaluation modules, and step size adjustment mechanisms. Through systematic testing, we achieved correct simulation outcomes that validate the method's effectiveness. Our implementation includes automated step size scaling with backtracking line search, where the algorithm iteratively reduces step size until satisfying both Wolfe-Powell conditions. Furthermore, we conducted comprehensive data analysis to better understand the obtained results, examining convergence patterns, iteration counts, and computational efficiency. The analysis module includes performance metrics calculation and comparative evaluation against alternative methods. We also discussed potential improvement directions, suggesting adaptive parameter tuning and hybrid approach combinations for enhanced performance. Overall, this work provides a complete optimization framework with valuable insights for research in related fields, offering practical code implementation strategies and algorithmic optimization techniques suitable for various nonlinear optimization scenarios.