An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of terms. The main idea of the algorithm is to solve a sequence of related problems, each involving finite samples of objective- and constraint-function terms, over which the sample sets grow progressively. Under assumptions about the problem functions and their first- and second-order derivatives that are reasonable in real-world settings of interest, it is shown that -- with sufficiently large initial sample sizes -- solving a sequence of problems defined through progressive sampling yields a better worst-case sample complexity bound compared to solving a single problem with the full sets of samples. The results of numerical experiments with a set of test problems demonstrate that the proposed approach can be effective in practice.

翻译：提出了一种算法，用于求解连续非线性等式约束优化问题，其中目标函数和约束函数由大量有限项上的期望或平均值定义。本文对该算法进行了分析并测试了其性能。该算法的主要思想是求解一系列相关的问题，每个问题涉及目标函数和约束函数项的有限样本，且样本集逐渐增大。在关于问题函数及其一阶和二阶导数符合实际场景的合理假设下，研究表明——当初始样本量足够大时——通过渐进采样求解一系列问题，相比使用全部样本集求解单个问题，可获得更优的最坏情况样本复杂度界。基于一组测试问题的数值实验结果表明，所提方法在实际中能够有效发挥作用。