A NEW CONJUGATE GRADIENT METHOD BASED ON LOGISTIC MAPPING FOR UNCONSTRAINED OPTIMIZATION AND ITS APPLICATION IN REGRESSION ANALYSIS

Abstract

The study tackles the critical need for efficient optimization techniques in unconstrained optimization problems, where conventional techniques often suffer from slow and inefficient convergence. There is still a need for algorithms that strike a balance between computational efficiency and robustness, despite advancements in gradient-based techniques. This work introduces a novel conjugate gradient algorithm based on the logistic mapping formula. As part of the methodology, descent conditions are established, and the suggested algorithm's global convergence properties are thoroughly examined. Comprehensive numerical experiments are used for empirical validation, and the new algorithm is compared to the Polak-Ribière-Polyak (PRP) algorithm. The suggested approach performs better than the PR algorithm, according to the results, and is more efficient since it needs fewer function evaluations and iterations to reach convergence. Furthermore, the usefulness of the suggested approach is demonstrated by its actual use in regression analysis, notably in the modelling of population estimates for the Kurdistan Region of Iraq. In contrast to conventional least squares techniques, the method maintains low relative error rates while producing accurate predictions. All things considered, this study presents the novel conjugate gradient algorithm as an effective tool for handling challenging optimisation problems in both theoretical and real-world contexts.