On Novel Conjugate Gradient Method for Solving Minimization Problems

Abstract

The secant condition constitutes a fundamental aspect of deriving the novel coefficient associated with the conjugate gradient method. The formulas proposed herein incorporate a golden ratio value of 0.618; and they demonstrate higher efficiency compared to conventional conjugate gradient methods. Concurrently, a comparative analysis was undertaken between the proposed formulas and the Pollack- Ribière (PR) method, which is broadly regarded as a robust and efficient strategy for addressing the challenges of unconstrained optimization. It delineates the performance metrics of the newly formulated simulated annealing (SA) algorithm as applied to two distinct scenarios (NI and NF), alongside the reference PR algorithm, which serves as a benchmark for performance evaluation. From the examination of these results, it can be inferred that the SA algorithm demonstrates consistent numerical behavior and attains favorable outcomes under specific conditions. However, the PR method persists as the most proficient overall and continues to function as a benchmark for performance evaluation.