# A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

arXiv: https://arxiv.org/abs/2304.14907 · HTML: https://mlsanity.com/paper/2304.14907/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2007.10525/) (2020)
- [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)
- [Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems](https://mlsanity.com/paper/2211.15943/) (2022)
- [Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2112.14799/) (2021)
- [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)
- [A Sequential Quadratic Programming Method for Optimization with Stochastic Objective Functions, Deterministic Inequality Constraints and Robust Subproblems](https://mlsanity.com/paper/2302.07947/) (2023)
- [Complexity Analysis of a Sampling-Based Interior Point Method for Convex Optimization](https://mlsanity.com/paper/1811.07677/) (2018)

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

- [Multi-Objective Preference Optimization: Improving Human Alignment of Generative Models](https://mlsanity.com/paper/2505.10892/) (2025)
- [No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations](https://mlsanity.com/paper/2305.03824/) (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)
- [L3Ms -- Lagrange Large Language Models](https://mlsanity.com/paper/2410.21533/) (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)

## Abstract (arXiv)

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth nonconvex optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique in its use of inner neighborhoods of the feasible region -- defined by a positive and vanishing neighborhood-parameter sequence -- in which the iterates are forced to remain. It is shown that with a careful balance between the barrier, step-size, and neighborhood sequences, the proposed algorithm satisfies convergence guarantees in both deterministic and stochastic settings. The results of numerical experiments show that in both settings the algorithm can outperform projection-based methods.