# Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

arXiv: https://arxiv.org/abs/2204.04161 · HTML: https://mlsanity.com/paper/2204.04161/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2022.

## Built on by (most cited first, 13 of 13)

- [Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems](https://mlsanity.com/paper/2211.15943/) (2022)
- [Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees](https://mlsanity.com/paper/2409.09906/) (2024)
- [A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2301.00477/) (2023)
- [A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems](https://mlsanity.com/paper/2304.14907/) (2023)
- [Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization](https://mlsanity.com/paper/2308.03687/) (2023)
- [Trust-Region Sequential Quadratic Programming for Stochastic Optimization with Random Models](https://mlsanity.com/paper/2409.15734/) (2024)
- [High Probability Complexity Bounds of Trust-Region Stochastic Sequential Quadratic Programming with Heavy-Tailed Noise](https://mlsanity.com/paper/2503.19091/) (2025)
- [Second-order Information Promotes Mini-Batch Robustness in Variance-Reduced Gradients](https://mlsanity.com/paper/2404.14758/) (2024)
- [A Trust-Region Interior-Point Stochastic Sequential Quadratic Programming Method](https://mlsanity.com/paper/2603.10230/) (2026)
- [Single-Loop Deterministic and Stochastic Interior-Point Algorithms for Nonlinearly Constrained Optimization](https://mlsanity.com/paper/2408.16186/) (2024)
- [Stochastic interior-point methods for smooth conic optimization with applications](https://mlsanity.com/paper/2412.12987/) (2024)
- [TRSVR: An Adaptive Stochastic Trust-Region Method with Variance Reduction](https://mlsanity.com/paper/2601.14647/) (2026)
- [TR-SSQP: A Trust-Region Method for Constrained Stochastic Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2609.30732/) (2026)

## Abstract (arXiv)

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that employs variance reduction in the gradient approximations. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our proposed algorithm converges to zero in expectation from arbitrary starting points, for both constant and adaptive step size strategies. Finally, we demonstrate the practical performance of our proposed algorithm on constrained binary classification problems that arise in machine learning.