A new framework for constrained optimization via feedback control of Lagrange multipliers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910005643444224 |
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| author | Cerone, V. Fosson, S. M. Pirrera, S. Regruto, D. |
| author_facet | Cerone, V. Fosson, S. M. Pirrera, S. Regruto, D. |
| contents | The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a feedback control system where the Lagrange multipliers are the control input, and the output represents the constraints. The system converges to a stationary point of the constrained optimization problem through suitable regulation. Regarding the Lagrange multipliers, we consider two control laws: proportional-integral control and feedback linearization. These choices give rise to a family of different methods. We rigorously develop the related algorithms, theoretically analyze their convergence and present several numerical experiments to support their effectiveness concerning the state-of-the-art approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new framework for constrained optimization via feedback control of Lagrange multipliers Cerone, V. Fosson, S. M. Pirrera, S. Regruto, D. Optimization and Control Systems and Control The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a feedback control system where the Lagrange multipliers are the control input, and the output represents the constraints. The system converges to a stationary point of the constrained optimization problem through suitable regulation. Regarding the Lagrange multipliers, we consider two control laws: proportional-integral control and feedback linearization. These choices give rise to a family of different methods. We rigorously develop the related algorithms, theoretically analyze their convergence and present several numerical experiments to support their effectiveness concerning the state-of-the-art approaches. |
| title | A new framework for constrained optimization via feedback control of Lagrange multipliers |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2403.12738 |