In the first result, we present graph neural networks (GNNs) that are capable of solving all linear programs (LPs) up to a given size, but this result fails to hold for mixed-integer linear programs (MILPs) since no GNN cannot distinguish certain pairs of different MILPs. In the second result, we impose certain "limit point" conditions to the neural networks for convex smooth+proximable optimization and obtain L2O algorithm-templates that are not only faster but also have better generalization performance. 

Joint work with Zi'ang Chen, Jialin Liu, Xiaohan Chen, and others.