  A sequential quadratic optimization algorithm is proposed for solving smooth
nonlinear equality constrained optimization problems in which the objective
function is defined by an expectation of a stochastic function. The algorithmic
structure of the proposed method is based on a step decomposition strategy that
is known in the literature to be widely effective in practice, wherein each
search direction is computed as the sum of a normal step (toward linearized
feasibility) and a tangential step (toward objective decrease in the null space
of the constraint Jacobian). However, the proposed method is unique from others
in the literature in that it both allows the use of stochastic objective
gradient estimates and possesses convergence guarantees even in the setting in
which the constraint Jacobians may be rank deficient. The results of numerical
experiments demonstrate that the algorithm offers superior performance when
compared to popular alternatives.
