Progressively Sampled Equality-Constrained Optimization
Abstract
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.
Cite
@article{arxiv.2510.00417,
title = {Progressively Sampled Equality-Constrained Optimization},
author = {Frank E. Curtis and Lingjun Guo and Daniel P. Robinson},
journal= {arXiv preprint arXiv:2510.00417},
year = {2026}
}