# Progressively Sampled Equality-Constrained Optimization

arXiv: https://arxiv.org/abs/2510.00417 · HTML: https://mlsanity.com/paper/2510.00417/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 3 of 3)

- [The Landscape of Empirical Risk for Non-convex Losses](https://mlsanity.com/paper/1607.06534/) (2016)
- [Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2007.10525/) (2020)
- [Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian](https://mlsanity.com/paper/2204.01448/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization](https://mlsanity.com/paper/2608.12665/) (2026)

## Abstract (arXiv)

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.