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.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Report number: | Lehigh ISE Technical Report 25T-017 |
| Cite as: | arXiv:2510.00417 [math.OC] |
| (or arXiv:2510.00417v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2510.00417 arXiv-issued DOI via DataCite |
Submission history
From: Frank E. Curtis [view email]
[v1]
Wed, 1 Oct 2025 01:58:17 UTC (651 KB)
[v2]
Wed, 13 May 2026 16:02:28 UTC (632 KB)