A Conjugate Gradient Algorithm for the Non-Convex Minimization Problem and Its Convergence Properties

Abstract

This study introduces a new and efficient modification of the conjugate gradient algorithm for solving non-convex unconstrained optimization problems. The proposed method ensures the sufficient descent property regardless of the line search technique and is proven to be globally convergent under both Wolfe and Armijo conditions. Its numerical performance is assessed through a set of large-scale benchmark problems. The findings indicate that the proposed algorithm exhibits competitive efficiency and reliability compared to existing conjugate gradient variants. To demonstrate applicability further, the algorithm is tested on two scenarios. The first is an image restoration problem, and the second is the motion control of a 2-DOF planar robotic manipulator, where inverse kinematics is solved iteratively for trajectory tracking. The algorithm demonstrates high tracking precision and stable convergence, highlighting its theoretical soundness and potential for various optimization applications.