To extend the proposed adaptive heavy ball method to handle other types of regularization functions beyond the strongly convex case, we can consider incorporating different types of regularization functions that are not strictly convex. One approach could be to modify the step-size and momentum coefficient selection criteria to accommodate the properties of the specific regularization function. For non-convex regularization functions, the optimization landscape may have multiple local minima, so the method may need to be adapted to navigate these challenges. Additionally, techniques such as stochastic approximation or adaptive learning rates could be employed to handle the non-convexity of the regularization function.