Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians

• Main Authors: Berahas, Albert S, Shi, Jiahao, Zhou, Baoyu
• Format: Journal Article
• Language: English
• Published: 09.03.2025
• Subjects: Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.2503.06702

We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result, is robust to potential rank-deficiency in the constraints, allows for two different step size strategies, and has an early stopping mechanism. Under the linear independence constraint qualification, convergence is established to a neighborhood of a first-order stationary point, where the radius of the neighborhood is proportional to the noise levels in the objective function and constraints. Moreover, in the rank-deficient setting, the merit parameter may converge to zero, and convergence to a neighborhood of an infeasible stationary point is established. Numerical experiments demonstrate the efficiency and robustness of the proposed method.