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:本文提出了一种顺序二次优化算法,用于解决平滑的非线性等式约束优化问题,其中目标函数由随机函数的期望定义。所提出的方法的算法结构基于一种在文献中被广泛认为是有效的步骤分解策略,其中每个搜索方向都被计算为正常步骤(朝向线性化可行性)和切向步骤(朝向约束雅可比矩阵的零空间内的目标减少)的和。然而,本文所提出的方法与文献中的其他方法不同,它既允许使用随机目标梯度估计,又具有收敛保证,即使在约束雅可比矩阵可能秩缺失的情况下。数值实验的结果表明,与流行的替代方法相比,该算法具有卓越的性能。