Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 374–396 | Cite as

Maximal Solutions of Sparse Analysis Regularization

  • Abdessamad Barbara
  • Abderrahim JouraniEmail author
  • Samuel Vaiter


This paper deals with the non-uniqueness of the solutions of an analysis—Lasso regularization. Most previous works in this area are concerned with the case, where the solution set is a singleton, or to derive guarantees to enforce uniqueness. Our main contribution consists in providing a geometrical interpretation of a solution with a maximal analysis support: such a solution abides in the relative interior of the solution set. Our result allows us to provide a way to exhibit a maximal solution using a primal-dual interior point algorithm.


Lasso Analysis sparsity Uniqueness Inverse problem Support identification Barrier penalization 

Mathematics Subject Classification

90C25 49J52 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université de Bourgogne Franche-ComtéDijonFrance
  2. 2.CNRSUniversité de Bourgogne Franche-ComtéDijonFrance

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