{"ID":2861797,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00417","arxiv_id":"2510.00417","title":"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.","short_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,...","url_abs":"https://arxiv.org/abs/2510.00417","url_pdf":"https://arxiv.org/pdf/2510.00417v2","authors":"[\"Frank E. Curtis\",\"Lingjun Guo\",\"Daniel P. Robinson\"]","published":"2025-10-01T01:58:17Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}