Progressively Sampled Equality-Constrained Optimization

Frank E. Curtis; Lingjun Guo; Daniel P. Robinson

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arXiv · 2510.00417

Progressively Sampled Equality-Constrained Optimization

Frank E. Curtis·Lingjun Guo·Daniel P. Robinson

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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.

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BibTeX RIS

Frank E. Curtis, Lingjun Guo, Daniel P. Robinson. 2025-10-01. Progressively Sampled Equality-Constrained Optimization. https://arxiv.org/abs/2510.00417

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