The inexact two-stepsize stochastic SQP algorithm achieves O(ε_c^{-2}) worst-case complexity for infeasibility without constraint qualifications and optimal O(ε_L^{-4}) for the Lagrangian gradient.
S., Bollapragada, R., and Zhou, B
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MoSSP is a new single-loop stochastic penalty method with Polyak or recursive momentum that achieves O(ε^{-4}) or O(ε^{-3}) oracle complexity for stochastic ε-KKT points in nonconvex constrained DC-regularized problems.
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Complexity of an inexact stochastic SQP algorithm for equality constrained optimization
The inexact two-stepsize stochastic SQP algorithm achieves O(ε_c^{-2}) worst-case complexity for infeasibility without constraint qualifications and optimal O(ε_L^{-4}) for the Lagrangian gradient.
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MoSSP: A Momentum-Based Single-Loop Stochastic Penalty Method for Nonconvex Constrained DC-Regularized Optimization
MoSSP is a new single-loop stochastic penalty method with Polyak or recursive momentum that achieves O(ε^{-4}) or O(ε^{-3}) oracle complexity for stochastic ε-KKT points in nonconvex constrained DC-regularized problems.