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The Sliding Frank-Wolfe Algorithm for the BLASSO

Q. Denoyelle, V. Duval, G. Peyré, E. Soubies

Proceedings of the Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS'19), Toulouse, French Republic, July 1-4, 2019, paper no. 172.

This paper showcases the Sliding Frank-Wolfe (SFW), which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is the continuous (i.e. off-thegrid or grid-less) counterpart of the well-known ℓ1 sparse regularisation method (also known as LASSO or Basis Pursuit). Our algorithm is a variation on the classical Frank-Wolfe (also known as conditional gradient) which follows a recent trend of interleaving convex optimization updates (corresponding to adding new spikes) with non-convex optimization steps (corresponding to moving the spikes). We prove theoretically that this algorithm terminates in a finite number of steps under a mild non-degeneracy hypothesis.

AUTHOR="Denoyelle, Q. and Duval, V. and Peyr{\'{e}}, G. and Soubies,
TITLE="The Sliding {F}rank-{W}olfe Algorithm for the {BLASSO}",
BOOKTITLE="Proceedings of the Workshop on Signal Processing with
        Adaptive Sparse Structured Representations ({SPARS'19})",
address="Toulouse, French Republic",
month="July 1-4,",
note="paper no.\ 172")

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