A Comparative Study of Optimization Techniques on the Rosenbrock Function

In the evolving landscape of artificial intelligence and machine learning, the choice of optimization algorithm can significantly impact the success of model training and the accuracy of predictions. This paper embarks on a rigorous and comprehensive exploration of widely adopted optimization techniques, specifically focusing on their performance when applied to the notoriously challenging Rosenbrock function. As a benchmark problem known for its deceptive curvature and narrow valleys, the Rosenbrock function provides a fertile ground for examining the nuances and intricacies of algorithmic behavior. The study delves into a diverse array of optimization methods, including traditional Gradient Descent, its stochastic variant (SGD), and the more sophisticated Gradient Descent with Momentum. The investigation further extends to adaptive methods like RMSprop, AdaGrad, and the highly regarded Adam optimizer. By meticulously analyzing and visualizing the optimization paths, convergence rates, and gradient norms, this paper uncovers critical insights into the strengths and limitations of each technique. Our findings not only illuminate the intricate dynamics of these algorithms but also offer actionable guidance for their deployment in complex, real-world optimization problems. This comparative analysis promises to intrigue and inspire researchers and practitioners alike, as it reveals the subtle yet profound impacts of algorithmic choices in the quest for optimization excellence.