New hybrid conjugate gradient method for mode function estimation

Abstract

Unconstrained optimization is a technique used to find the best possible solution or optimal value for a given problem, often in the context of minimizing or maximizing a function. These methods are fundamental in various fields such as engineering, economics, machine learning, and operations research. Conjugate gradient methods are very important methods for solving unconstrain optimization Problems, especial when the dimension is large. In this thesis, based on the hybrid conjugate gradient method, a new family of gradient methods are proposed for solving unconstrained optimization. By using wolfe line-search conditions, these changes aim to improve the algorithms’ convergence features and accelerate the descent direction. Our studies’ numerical results offer strong eviddence of the robustness and efficiency of these new methods compared to existing conjugate gradient methods. We conducted thorough numerical studies to validate our proposed methods.we have demonstrated through numerical tests that the suggested are more effective and perform better than the combined algorithms after demonstrating their convergence using experimental functions. Additionally, the proposed algorithms were expanded to address challenges in nonparametric statistics, specifically focusing on the problems of the mode function.