# A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization

arXiv: https://arxiv.org/abs/2301.00477 · HTML: https://mlsanity.com/paper/2301.00477/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 1 Jan 2023.

## Builds on (most cited first, 20 of 20)

- [Variance-Reduced and Projection-Free Stochastic Optimization](https://mlsanity.com/paper/1602.02101/) (2016)
- [Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2007.10525/) (2020)
- [Global convergence rate analysis of unconstrained optimization methods based on probabilistic models](https://mlsanity.com/paper/1505.06070/) (2015)
- [Stochastic Optimization Using a Trust-Region Method and Random Models](https://mlsanity.com/paper/1504.04231/) (2015)
- [An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians](https://mlsanity.com/paper/2102.05320/) (2021)
- [A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians](https://mlsanity.com/paper/2106.13015/) (2021)
- [Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2112.14799/) (2021)
- [Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming](https://mlsanity.com/paper/2109.11502/) (2021)
- [Global Convergence Rate Analysis of a Generic Line Search Algorithm with Noise](https://mlsanity.com/paper/1910.04055/) (2019)
- [Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction](https://mlsanity.com/paper/2204.04161/) (2022)
- [Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints](https://mlsanity.com/paper/2107.03512/) (2021)
- [An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2206.00712/) (2022)
- [Convergence of trust-region methods based on probabilistic models](https://mlsanity.com/paper/1304.2808/) (2013)
- [Generalized Stochastic Frank-Wolfe Algorithm with Stochastic "Substitute" Gradient for Structured Convex Optimization](https://mlsanity.com/paper/1807.07680/) (2018)
- [First- and Second-Order High Probability Complexity Bounds for Trust-Region Methods with Noisy Oracles](https://mlsanity.com/paper/2205.03667/) (2022)
- [Derivative-Free Optimization of Noisy Functions via Quasi-Newton Methods](https://mlsanity.com/paper/1803.10173/) (2018)
- [Constrained Optimization in the Presence of Noise](https://mlsanity.com/paper/2110.04355/) (2021)
- [Direct search based on probabilistic descent in reduced spaces](https://mlsanity.com/paper/2204.01275/) (2022)
- [High Probability Complexity Bounds for Adaptive Step Search Based on Stochastic Oracles](https://mlsanity.com/paper/2106.06454/) (2021)
- [Linesearch Newton-CG methods for convex optimization with noise](https://mlsanity.com/paper/2205.06710/) (2022)

## Built on by (most cited first, 8 of 8)

- [Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimization](https://mlsanity.com/paper/2301.13314/) (2023)
- [Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints](https://mlsanity.com/paper/2504.15243/) (2025)
- [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)
- [A Trust-Region Interior-Point Stochastic Sequential Quadratic Programming Method](https://mlsanity.com/paper/2603.10230/) (2026)
- [A Trust-Region Algorithm for Noisy Equality Constrained Optimization](https://mlsanity.com/paper/2411.02665/) (2024)
- [TR-SSQP: A Trust-Region Method for Constrained Stochastic Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2609.30732/) (2026)

## Abstract (arXiv)

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic approximations of the objective function and its associated derivatives can be computed via inexact probabilistic zeroth- and first-order oracles. Under reasonable assumptions, a high-probability bound on the iteration complexity of the algorithm to approximate first-order stationarity is derived. Numerical results on standard nonlinear optimization test problems illustrate the advantages and limitations of our proposed method.