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Pré-Publication, Document De Travail Année : 2024

Inertial Quasi-Newton Methods for Monotone Inclusions: Efficient Resolvent Calculus and Primal-Dual Algorithms

Résumé

We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent operator. A change of the metric makes its computation even harder, and this is even true for a simple operator whose resol- vent is known for the standard metric. In order to fully exploit the advantage of adapting the metric, we develop a new efficient resolvent calculus for a low-rank perturbed standard metric, which accounts exactly for quasi-Newton metrics. Moreover, we prove the convergence of our algorithms, including linear convergence rates in case one of the two considered oper- ators is strongly monotone. As a by-product of our general monotone inclusion framework, we instantiate a novel inertial quasi-Newton Primal-Dual Hybrid Gradient Method (PDHG) for solving saddle point problems. The favourable performance of our inertial quasi-Newton PDHG method is demonstrated on several numerical experiments in image processing.
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hal-04506477 , version 1 (15-03-2024)

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  • HAL Id : hal-04506477 , version 1

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Shida Wang, Jalal M. Fadili, Peter Ochs. Inertial Quasi-Newton Methods for Monotone Inclusions: Efficient Resolvent Calculus and Primal-Dual Algorithms. 2024. ⟨hal-04506477⟩
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