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.

翻译：提出了一种序列二次优化算法，用于求解目标函数由随机函数期望定义的光滑非线性等式约束优化问题。该方法基于文献中已知在实践中广泛有效的步长分解策略构建算法结构，其中每个搜索方向计算为法向步（朝向线性化可行性）与切向步（在约束雅可比矩阵零空间中减小目标函数）之和。然而，所提方法在文献中具有独特性：它既允许使用随机目标梯度估计，又能在约束雅可比矩阵可能秩亏的情况下提供收敛保证。数值实验结果表明，该算法相比流行的替代方法展现出更优的性能。