Regularized dynamical systems associated with structured monotone inclusions

Abstract: In this report, we consider two dynamical systems associated with additively structured monotone inclusions involving a multi-valued maximally monotone operator $\mathcal{A}$ and a single-valued operator $\mathcal{B}$ in real Hilbert spaces.

We established strong convergence of the regularized forward-backward and regularized forward - backward–forward dynamics to an “optimal” solution of the original inclusion under a weak assumption on the single-valued operator $\mathcal{B}$.

Convergence estimates are obtained if the composite operator $\mathcal{A} + \mathcal{B}$ is maximally monotone and strongly (pseudo)monotone. Time-discretization of the corresponding continuous dynamics provides an iterative regularization forward-backward method or an iterative regularization forward-backward-forward method with relaxation parameters. Some simple numerical examples were given to illustrate the agreement between analytical and numerical results as well as the performance of the proposed algorithms.

optimization and control

Audience: researchers in the topic

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