Low-dose computed tomography (LDCT) aims to minimize the radiation exposure to patients while maintaining diagnostic image quality. However, traditional CT reconstruction algorithms often struggle with the ill-posed nature of the problem, resulting in severe image artifacts. Recent advances in optimization-based deep learning algorithms offer promising solutions to improve LDCT reconstruction. In this paper, we explore learnable optimization algorithms (LOA) for CT reconstruction, which integrate deep learning within variational models to enhance the regularization process. These methods, including LEARN++ and MAGIC, leverage dual-domain networks that optimize both image and sinogram data, significantly improving reconstruction quality. We also present proximal gradient descent and ADMM-inspired networks, which are efficient and theoretically grounded approaches. Our results demonstrate that these learnable methods outperform traditional techniques, offering enhanced artifact reduction, better detail preservation, and robust performance in clinical scenarios.