具有秩亏雅可比矩阵的非线性等式约束优化随机顺序二次优化算法

IF 1.4 3区 数学 Q2 MATHEMATICS, APPLIED Mathematics of Operations Research Pub Date : 2023-10-30 DOI:10.1287/moor.2021.0154
Albert S. Berahas, Frank E. Curtis, Michael J. O'Neill, Daniel P. Robinson
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引用次数: 20

摘要

针对目标函数由期望定义的光滑非线性等式约束优化问题,提出了一种顺序二次优化算法。所提出方法的算法结构基于一种阶梯分解策略,该策略在文献中被认为在实践中广泛有效,其中每个搜索方向被计算为一个正方向(线性化可行性方向)和一个切向方向(约束雅可比矩阵零空间的目标减小方向)的和。然而,所提出的方法与文献中其他方法的独特之处在于,它既允许使用随机客观梯度估计,并且即使在约束雅可比矩阵可能缺乏秩的情况下也具有收敛性保证。数值实验结果表明,与现有的算法相比,该算法具有更好的性能。资助:本材料基于美国国家科学基金会计算与通信基金会分部资助的工作[CF-1740796],由海军研究办公室资助的工作[N00014-21-1-2532],以及由国家科学基金会资助的工作[2030859]给计算研究协会的CIFellows项目。
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A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians
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.
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来源期刊
Mathematics of Operations Research
Mathematics of Operations Research 管理科学-应用数学
CiteScore
3.40
自引率
5.90%
发文量
178
审稿时长
15.0 months
期刊介绍: Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.
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