Random-Subspace Sequential Quadratic Programming for Constrained Zeroth-Order Optimization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911563204526080 |
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| author | Zhang, Runyu Zardini, Gioele |
| author_facet | Zhang, Runyu Zardini, Gioele |
| contents | We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making it difficult to simultaneously achieve computational efficiency and accurate constraint satisfaction. We propose a zeroth-order random-subspace sequential quadratic programming method (ZO-RS-SQP) that combines two-point directional estimation with low-dimensional SQP updates. At each iteration, the method samples a random low-dimensional subspace, estimates the projected objective gradient and constraint Jacobians using two-point evaluations, and solves a reduced quadratic program to compute the step. As a result, the per-iteration evaluation cost scales with the subspace dimension rather than the ambient dimension, while retaining the structured linearized-constraint treatment of SQP. We also consider an Armijo line-search variant that improves robustness in practice. Under standard smoothness and regularity assumptions, we establish convergence to first-order KKT points with high probability. Numerical experiments illustrate the effectiveness of the proposed approach on nonlinear constrained problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random-Subspace Sequential Quadratic Programming for Constrained Zeroth-Order Optimization Zhang, Runyu Zardini, Gioele Optimization and Control We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making it difficult to simultaneously achieve computational efficiency and accurate constraint satisfaction. We propose a zeroth-order random-subspace sequential quadratic programming method (ZO-RS-SQP) that combines two-point directional estimation with low-dimensional SQP updates. At each iteration, the method samples a random low-dimensional subspace, estimates the projected objective gradient and constraint Jacobians using two-point evaluations, and solves a reduced quadratic program to compute the step. As a result, the per-iteration evaluation cost scales with the subspace dimension rather than the ambient dimension, while retaining the structured linearized-constraint treatment of SQP. We also consider an Armijo line-search variant that improves robustness in practice. Under standard smoothness and regularity assumptions, we establish convergence to first-order KKT points with high probability. Numerical experiments illustrate the effectiveness of the proposed approach on nonlinear constrained problems. |
| title | Random-Subspace Sequential Quadratic Programming for Constrained Zeroth-Order Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.02202 |