Abstract: I will motivate and provide an overview of recent efforts in my research group on the design and analysis of stochastic-gradient-based algorithms for solving constrained optimization problems. I will focus in particular on our motivation for informed supervised learning, where constraints in the training problem can be used to impose prior knowledge on the properties that should be possessed by a trained prediction model. In addition, I will provide a detailed look at our newest extensions of heavy-ball and Adam schemes from the unconstrained to the equality-constrained setting, for which we have shown state-of-the-art convergence guarantees. I will demonstrate the impressive practical performance of our methods using a few informed supervised learning problems.