<p>In recent years, constrained minimization problems have received attention from researchers due to its widespread application fields such as image processing, network control, and machine learning. The gradient projection algorithm, as an effective algorithm for solving constrained minimization problems, has attracted much attention due to its multiple advantages. However, the gradient projection algorithm exhibits the disadvantage of slow convergence rate. To improve convergence rate, we propose three momentum-accelerated scaled gradient projection algorithms, including the Nesterov accelerated scaled gradient projection (NASGP), the unified momentum accelerated scaled gradient projection (UMASGP), and the symplectic accelerated scaled gradient projection (SASGP) algorithms, respectively. In the NASGP algorithm, a momentum term is employed to predict position in the gradient descent process, which facilitates the accelerated convergence of the algorithm. In the UMASGP algorithm, multiple momentum strategies are integrated to adapt to different gradient characteristics. In the SASGP algorithm, a well-known stable integrator based on symplectic and contact geometries is introduced to further enhance the system stability and accelerate convergence. These algorithms seek to more effectively tackle specific constrained minimization problems, such as image deblurring and binary classification. We conduct a large number of numerical experiments, to demonstrate the robustness and adaptability of our proposed algorithms.</p>