Medical image registration has a significant role in several applications. It has sequential processes, including transformation, similarity metric calculation, diffusion regularization, and optimization of the transformation parameters (i.e., rotation, translation, and shear). The optimization process for determining the optimal set of the transformation vectors is considered the main stage affecting the performance of the registration process. Hence, medical image registration can be deliberated as an optimization problem for computing the geometric transformations to realize maximum similarity between the moving image and the fixed one. In this paper a mono-modal nonrigid image registration using B-spline is designed for the alignment of Computed Tomography (CT) images using Adaptive Gradient algorithm (AdaGrad) optimizer. In addition, a comparative study with other first order optimizers, such as Stochastic Gradient Descent (SGD), Adaptive Moment Estimation (Adam) algorithm (AdaMaX), AdamP, and RangerQH were conducted. Also, a comparison with the limited memory Broyden-Fletcher-Goldfarb-Shannon (LBFGS) as a second order optimizer was also carried out. The results showed the superiority of the AdaGrad optimizer by 56.99% and 48.37% improvement in the target registration error (TRE) compared to the SGD, and the LBFGS optimizer, respectively.