A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians
A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians
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DOI：
10.1287/moor.2021.0154
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发表时间：
2021-06
影响因子：
1.7
通讯作者：
A. Berahas;Frank E. Curtis;Michael O'Neill;Daniel P. Robinson
中科院分区：
文献类型：
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作者：
A. Berahas;Frank E. Curtis;Michael O'Neill;Daniel P. Robinson
提出了一种序列二次优化算法，用于求解目标函数由期望定义的光滑非线性等式约束优化问题。所提方法的算法结构基于一种在文献中已知在实践中广泛有效的步分解策略，其中每个搜索方向计算为法向步（朝着线性化可行性）和切向步（朝着约束雅可比矩阵零空间中的目标下降）之和。然而，所提方法与文献中的其他方法不同之处在于，它既允许使用随机目标梯度估计，并且即使在约束雅可比矩阵可能秩亏的情况下也具有收敛保证。数值实验结果表明，与流行的替代方法相比，该算法具有优越的性能。资助：本材料基于美国国家科学基金会计算与通信基础部门在[CF - 1740796]奖项下、海军研究办公室在[N00014 - 21 - 1 - 2532]奖项下以及美国国家科学基金会在[2030859]奖项下对计算研究协会CIFellows项目的支持工作。
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. 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 with popular alternatives. Funding: This material is based upon work supported by the U.S. National Science Foundation’s Division of Computing and Communication Foundations under award [CF-1740796], by the Office of Naval Research under award [N00014-21-1-2532], and by the National Science Foundation under award [2030859] to the Computing Research Association for the CIFellows Project.