I will present recent work by my research group on the design and analysis of stochastic-gradient-based algorithms for solving nonconvex constrained optimization problems, which may arise, for example, in informed supervised learning.  I will focus in particular on algorithmic strategies that have consistently been shown to exhibit the best practical performance, rather than focus on regularization-based methods that are popular for theoretical analyses, but often fail to yield satisfactory results.  Our algorithms possess solid theoretical convergence guarantees and preliminary experiments motivate continued study.