Fixed-time-stable ODE Representation of Lasso
This provides a new computational framework for solving Lasso problems, which is incremental as it builds on existing ODE representations by adding fixed-time stability.
The paper tackles the Lasso problem by proposing a fixed-time-stable ordinary differential equation (ODE) representation, enabling solution on analog computers and neurophysiological interpretation, with numerical experiments showing the trajectory reaches the optimal solution within a prescribed time independent of problem data.
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.