Implementation and Comparative Analysis of AMGT Method in Maple 24: Convergence Performance in Optimization Problems

Abstract

This study investigates the utilization of the Accelerated Modified Gradient Technique (AMGT) in Maple 24 for optimization problem-solving. The research focuses on enhancing and evaluating the convergence speed of AMGT in comparison to the Gradient Descent (GD) and Conjugate Gradient (CG) methods. The analysis covers a range of function types, such as convex functions (e.g., production cost, energy consumption, and transportation cost functions) and a non-convex function. Findings showcase the effectiveness and versatility of AMGT, shedding light on its utility for addressing practical optimization challenges.