Explore stochastic-gradient-based algorithms for solving constrained continuous optimization problems in this 29-minute talk by Frank Curtis at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the design, analysis, and practical performance of these algorithms, particularly in the context of constrained machine learning model training. Learn about stochastic interior-point and sequential-quadratic-programming algorithms, their convergence guarantees under loose assumptions, and their application to physics-informed and fair learning problems. Gain insights from numerical experiments demonstrating the effectiveness of these proposed techniques in real-world scenarios.