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An algorithm is proposed, analyzed, and tested experimentally for solvingstochastic optimization problems in which the decision variables areconstrained to satisfy equations defined by deterministic, smooth, andnonlinear functions. It is assumed that constraint function and derivativevalues can be computed, but that only stochastic approximations are availablefor the objective function and its derivatives. The algorithm is of thesequential quadratic optimization variety. A distinguishing feature of thealgorithm is that it allows inexact subproblem solutions to be employed, whichis particularly useful in large-scale settings when the matrices defining thesubproblems are too large to form and/or factorize. Conditions are imposed onthe inexact subproblem solutions that account for the fact that only stochasticobjective gradient estimates are available. Convergence results in expectationare established for the method. Numerical experiments show that it outperformsan alternative algorithm that employs highly accurate subproblem solutions inevery iteration.

Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints