Selection of Mathematical Optimization Methods for Solving Engineering Practice Problems

Optimization theory plays a pivotal role in contemporary scientific and technical endeavors, permeating various engineering disciplines. From fine-tuning chemical-technological systems to optimizing production processes, the application of optimal management techniques is widespread, particularly in the context of complex automation and sophisticated technical setups. The primary goal of optimization is to identify the most optimal solution among numerous potential outcomes, employing diverse strategies ranging from analytical methodologies to numerical simulations. This paper explores the efficacy of the fastest ascent method in approaching the extremum of the Rosenbrock function, emphasizing the importance of selecting appropriate starting coordinates. Furthermore, the study investigates the impact of errors introduced through random variables, highlighting the need for robust methodologies capable of navigating uncertainties. Through comprehensive analysis and experimentation, this research contributes to the ongoing discourse surrounding optimization methodologies, shedding light on their effectiveness and applicability in diverse engineering contexts.