  A sequential quadratic optimization algorithm for minimizing an objective
function defined by an expectation subject to nonlinear inequality and equality
constraints is proposed, analyzed, and tested. The context of interest is when
it is tractable to evaluate constraint function and derivative values in each
iteration, but it is intractable to evaluate the objective function or its
derivatives in any iteration, and instead an algorithm can only make use of
stochastic objective gradient estimates. Under loose assumptions, including
that the gradient estimates are unbiased, the algorithm is proved to possess
convergence guarantees in expectation. The results of numerical experiments are
presented to demonstrate that the proposed algorithm can outperform an
alternative approach that relies on the ability to compute more accurate
gradient estimates.
