A Trust-Region Interior-Point Stochastic Sequential Quadratic Programming Method

2026-03-10

AI Summary

This work addresses optimization problems characterized by a stochastic objective function whose gradients cannot be computed exactly, along with deterministic nonlinear equality and inequality constraints. The paper proposes a novel algorithmic framework that, for the first time, integrates trust-region methods, interior-point techniques, and stochastic sequential quadratic programming (SSQP). At each iteration, the method constructs a stochastic oracle satisfying an adaptive accuracy condition and updates the barrier parameter via a prescribed decaying sequence to handle inequality constraints. Under standard assumptions, the algorithm is proven to converge almost surely to a first-order stationary point. Its efficacy is demonstrated through numerical experiments on a subset of the CUTEst test set and logistic regression problems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality constraints. In this setting, exact evaluations of the objective function and its gradient are unavailable, but their stochastic estimates can be constructed. In particular, at each iteration our method builds stochastic oracles, which estimate the objective value and gradient to satisfy proper adaptive accuracy conditions with a fixed probability. To handle inequality constraints, we adopt an interior-point method (IPM), in which the barrier parameter follows a prescribed decaying sequence. Under standard assumptions, we establish global almost-sure convergence of the proposed method to first-order stationary points. We implement the method on a subset of problems from the CUTEst test set, as well as on logistic regression problems, to demonstrate its practical performance.

Problem

• stochastic optimization
• nonlinear constraints
• sequential quadratic programming
• interior-point method
• trust-region method

Innovation

• trust-region
• interior-point method
• stochastic sequential quadratic programming
• stochastic oracles
• global almost-sure convergence