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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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.