A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917382687031296 |
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| author | Li, Mengmou Zhou, Yu Shen, Xun Nagahara, Masaaki |
| author_facet | Li, Mengmou Zhou, Yu Shen, Xun Nagahara, Masaaki |
| contents | This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback. The proposed canonical structure is obtained through a simple linear transformation. It enables a direct extension from unconstrained optimization algorithms to set-constrained ones through projection in a Lyapunov-induced norm. The resulting projected algorithms attain the optimal solution while preserving the convergence rates of their unconstrained counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02762 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback Li, Mengmou Zhou, Yu Shen, Xun Nagahara, Masaaki Optimization and Control Systems and Control This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback. The proposed canonical structure is obtained through a simple linear transformation. It enables a direct extension from unconstrained optimization algorithms to set-constrained ones through projection in a Lyapunov-induced norm. The resulting projected algorithms attain the optimal solution while preserving the convergence rates of their unconstrained counterparts. |
| title | A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.02762 |