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Maximal Solutions of Sparse Analysis Regularization

Author

Listed:
  • Abdessamad Barbara

    (Université de Bourgogne Franche-Comté)

  • Abderrahim Jourani

    (Université de Bourgogne Franche-Comté)

  • Samuel Vaiter

    (Université de Bourgogne Franche-Comté)

Abstract

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.

Suggested Citation

  • Abdessamad Barbara & Abderrahim Jourani & Samuel Vaiter, 2019. "Maximal Solutions of Sparse Analysis Regularization," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 374-396, February.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1385-3
    DOI: 10.1007/s10957-018-1385-3
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Hui Zhang & Wotao Yin & Lizhi Cheng, 2015. "Necessary and Sufficient Conditions of Solution Uniqueness in 1-Norm Minimization," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 109-122, January.
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