Relaxations for Non-Separable Cardinality/Rank Penalties
Paper i proceeding, 2021

Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can be described as separable, meaning that they apply a penalty to each element (or singular value) based on size, without considering the joint distribution. In this paper we present a class of non-separable penalties and give a recipe for computing strong relaxations suitable for optimization. In our analysis of this formulation we first give conditions that ensure that the global ly optimal solution of the relaxation is the same as that of the original (unrelaxed) objective. We then show how a stationary point can be guaranteed to be unique under the restricted isometry property (RIP) assumption.1


Carl Olsson

Lunds universitet

Datorseende och medicinsk bildanalys

Daniele Gerosa

Lunds universitet

Marcus Carlsson

Lunds universitet

Proceedings of the IEEE International Conference on Computer Vision

15505499 (ISSN)

Vol. 2021-October 162-171
9781665401913 (ISBN)

18th IEEE/CVF International Conference on Computer Vision Workshops, ICCVW 2021
Virtual, Online, Canada,

Optimeringsmetoder med prestandagarantier för maskininlärningsmetoder

Vetenskapsrådet (VR) (2018-05375), 2019-01-01 -- 2022-12-31.



Sannolikhetsteori och statistik

Matematisk analys



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