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arXiv · 2607.09495

Inertial forward-backward algorithm with exterior penalization and Tikhonov regularization

Siqi Qu·Juan Peypouquet·Mathias Staudigl
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Abstract

In a real Hilbertian setting, we develop in this paper numerical splitting techniques guaranteeing strong convergence to the least norm solution of constrained variational inequalities. We develop a multiscale inertial forward-backward splitting algorithm for solving constrained monotone inclusion problems with multiscale penalization and vanishing Tikhonov regularization. The proposed framework accommodates smooth, nonsmooth, and mixed smooth--nonsmooth penalty operators, providing a unified treatment of a broad class of constrained monotone inclusion problems. In this general framework, we establish weak convergence of the generated iterates. By introducing a discrete Tikhonov central path, we further prove strong convergence to the minimum-norm solution of the problem under a mild constraint qualification condition on the problem data.

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Siqi Qu, Juan Peypouquet, Mathias Staudigl. 2026-07-10. Inertial forward-backward algorithm with exterior penalization and Tikhonov regularization. https://arxiv.org/abs/2607.09495

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