Development of a New Conjugate Gradient Algorithm for Solving an Unconstrained Nonlinear Optimization Problem

Abstract

This article develops a new conjugate gradient algorithm in a scaled conjugate gradient field. The proposal depends on the following algorithms: Quasi-Newton and classical conjugate gradient. Under certain assumptions, the developed algorithm satisfies the descent direction and global convergence property. Additionally, the hybrid scaled gradient algorithm is involved in the new direction. Compared to the classical algorithm, the numerical outcomes demonstrate the superiority of our algorithm in tackling unconstrained nonlinear optimization problems.