Strong convergence of an inertial Tikhonov regularized dynamical system governed by a maximally comonotone operator (2411.19693v1)

Abstract: In a Hilbert framework, we consider an inertial Tikhonov regularized dynamical system governed by a maximally comonotone operator, where the damping coefficient is proportional to the square root of the Tikhonov regularization parameter. Under an appropriate setting of the parameters, we prove the strong convergence of the trajectory of the proposed system towards the minimum norm element of zeros of the underlying maximally comonotone operator. When the Tikhonov regularization parameter reduces to $\frac{1}{t^q}$ with $0<q<1$, we further establish some convergence rate results of the trajectories. Finally, the validity of the proposed dynamical system is demonstrated by a numerical example.