A new Polyak-momentum augmented Lagrangian algorithm achieves O(ε^{-4}) stochastic gradient complexity for ε-stationary solutions in linearly constrained nonconvex problems under standard stochastic assumptions.
V ariance-reduced first-orde r methods for deterministically constrained stochastic nonconvex o ptimization with strong convergence guarantees
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A Momentum-based Stochastic Algorithm for Linearly Constrained Nonconvex Optimization
A new Polyak-momentum augmented Lagrangian algorithm achieves O(ε^{-4}) stochastic gradient complexity for ε-stationary solutions in linearly constrained nonconvex problems under standard stochastic assumptions.