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Second Order Splitting Dynamics with Vanishing Damping for Additively Structured Monotone Inclusions.
- Source :
- Journal of Dynamics & Differential Equations; Mar2024, Vol. 36 Issue 1, p727-756, 30p
- Publication Year :
- 2024
-
Abstract
- In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator A and a cocoercive operator B. We study the asymptotic behaviour of the trajectories generated by a second order equation with vanishing damping, attached to this problem, and governed by a time-dependent forward–backward-type operator. This is a splitting system, as it only requires forward evaluations of B and backward evaluations of A. A proper tuning of the system parameters ensures the weak convergence of the trajectories to the set of zeros of A + B , as well as fast convergence of the velocities towards zero. A particular case of our system allows to derive fast convergence rates for the problem of minimizing the sum of a proper, convex and lower semicontinuous function and a smooth and convex function with Lipschitz continuous gradient. We illustrate the theoretical outcomes by numerical experiments. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 36
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 175720194
- Full Text :
- https://doi.org/10.1007/s10884-022-10160-3