Fixed-time-stable ODE Representation of Lasso
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908933557321728 |
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| author | Wu, Liang Che, Yunhong Tan, Wallace Gian Yion Iliakis, Efstathios Braatz, Richard D. Drgoňa, Ján |
| author_facet | Wu, Liang Che, Yunhong Tan, Wallace Gian Yion Iliakis, Efstathios Braatz, Richard D. Drgoňa, Ján |
| contents | Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE) representation of the Lasso problem not only enables its solution on analog computers but also provides a framework for interpreting neurophysiological phenomena. This article proposes a fixed-time-stable ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based fixed-time-stable ODE system for solving the corresponding Karush-Kuhn-Tucker (KKT) conditions. Moreover, the settling time of the ODE is independent of the problem data and can be arbitrarily prescribed. Numerical experiments verify that the trajectory reaches the optimal solution within the prescribed time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02069 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixed-time-stable ODE Representation of Lasso Wu, Liang Che, Yunhong Tan, Wallace Gian Yion Iliakis, Efstathios Braatz, Richard D. Drgoňa, Ján Optimization and Control Systems and Control Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE) representation of the Lasso problem not only enables its solution on analog computers but also provides a framework for interpreting neurophysiological phenomena. This article proposes a fixed-time-stable ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based fixed-time-stable ODE system for solving the corresponding Karush-Kuhn-Tucker (KKT) conditions. Moreover, the settling time of the ODE is independent of the problem data and can be arbitrarily prescribed. Numerical experiments verify that the trajectory reaches the optimal solution within the prescribed time. |
| title | Fixed-time-stable ODE Representation of Lasso |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.02069 |