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A worst-case complexity bound is proved for a sequential quadraticoptimization (commonly known as SQP) algorithm that has been designed forsolving optimization problems involving a stochastic objective function anddeterministic nonlinear equality constraints. Barring additional terms thatarise due to the adaptivity of the monotonically nonincreasing merit parametersequence, the proved complexity bound is comparable to that known for thestochastic gradient algorithm for unconstrained nonconvex optimization. Theoverall complexity bound, which accounts for the adaptivity of the meritparameter sequence, shows that a result comparable to the unconstrained setting(with additional logarithmic factors) holds with high probability.

Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization