On Tikhonov-Regularized Doubly Nonlinear Dynamics with Dry Friction for Maximal Comonotone Inclusions

초록

Dynamical approximation has been widely recognized as a crucial numerical approach for solving monotone inclusion problems, and the ρ-comonotone operator is a generalization of the classical monotone one. A unified dynamical analysis framework for solving the ρ-comonotone inclusion problem is established in this paper. Specifically, firstly, an analytical link is constructed between the ρ-comonotone inclusion problem and a dynamical system with Tikhonov regularization, which demonstrates that the solutions of the latter asymptotically approximate those of the former as time tends to infinity. Secondly, explicit convergence rates of the dynamical system are derived under different decay conditions of the Tikhonov regularization term. Additionally, these results are applied to solve a class of nonsmooth convex optimization problems. Finally, a Runge–Kutta discretization algorithm corresponding to the continuous dynamical system is presented and its effectiveness is validated through several numerical examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

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