[Evaluate students' ability to analyze and compare theoretical convergence guarantees and empirical performance of proximal splitting methods (ADMM, FISTA, Douglas–Rachford) for convex and nonconvex composite optimization in Hilbert spaces. Scope: required assumptions (convexity, strong convexity, Lipschitz gradients, monotone operators, KL property), convergence rates versus asymptotic/stationary results, parameter/step-size selection, acceleration and restart strategies, implementation subtleties in infinite-dimensional settings, and the design and interpretation of numerical experiments demonstrating practical behavior.]