Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909532415852544 |
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| author | Berahas, Albert S. Shi, Jiahao Zhou, Baoyu |
| author_facet | Berahas, Albert S. Shi, Jiahao Zhou, Baoyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians Berahas, Albert S. Shi, Jiahao Zhou, Baoyu Optimization and Control 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. |
| title | Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.06702 |