An efficient gradient-based algorithm with descent direction for unconstrained optimization with applications to image restoration and robotic motion control

This study presents a novel gradient-based algorithm designed to enhance the performance of optimization models, particularly in computer science applications such as image restoration and robotic motion control. The proposed algorithm introduces a modified conjugate gradient (CG) method, ensuring the CG coefficient, β κ, remains integral to the search direction, thereby maintaining the descent property under appropriate line search conditions. Leveraging the strong Wolfe conditions and assuming Lipschitz continuity, we establish the global convergence of the algorithm. Computational experiments demonstrate the algorithm's superior performance across a range of test problems, including its ability to restore corrupted images with high precision and effectively manage motion control in a 3DOF robotic arm model. These results underscore the algorithm's potential in addressing key challenges in image processing and robotics.