  An algorithm is proposed, analyzed, and tested experimentally for solving
stochastic optimization problems in which the decision variables are
constrained to satisfy equations defined by deterministic, smooth, and
nonlinear functions. It is assumed that constraint function and derivative
values can be computed, but that only stochastic approximations are available
for the objective function and its derivatives. The algorithm is of the
sequential quadratic optimization variety. A distinguishing feature of the
algorithm is that it allows inexact subproblem solutions to be employed, which
is particularly useful in large-scale settings when the matrices defining the
subproblems are too large to form and/or factorize. Conditions are imposed on
the inexact subproblem solutions that account for the fact that only stochastic
objective gradient estimates are available. Convergence results in expectation
are established for the method. Numerical experiments show that it outperforms
an alternative algorithm that employs highly accurate subproblem solutions in
every iteration.
