MATLAB Optimization Using Complex Method Algorithm

This paper introduces a novel MATLAB implementation of the Complex Method optimization algorithm designed for solving nonlinear programming problems with constraints. The Complex Method is a widely-used optimization technique that delivers efficient and accurate results when handling nonlinear optimization challenges. The key advantages of this implementation include exceptional computational performance and optimization accuracy, achieved through sophisticated constraint-handling mechanisms and adaptive parameter tuning. The program incorporates several advanced features such as interactive visualization tools for monitoring convergence patterns and comprehensive analysis functions that provide detailed insights into optimization progress. The implementation utilizes MATLAB's built-in matrix operations for efficient complex formation and geometrical transformations, while employing penalty function methods for effective constraint management. Key algorithmic components include vertex generation, reflection operations, and contraction mechanisms that ensure robust convergence properties. Additional technical features include real-time performance metrics display, convergence criteria customization, and export capabilities for optimization results. The code structure follows modular design principles, allowing users to easily modify constraint definitions or objective functions according to their specific problem requirements. This powerful yet user-friendly tool provides researchers and engineers with an effective solution for various constrained nonlinear optimization scenarios, combining mathematical rigor with practical implementation efficiency.