Maximal Solutions of Sparse Analysis Regularization

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.
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Submitted on : Tuesday, February 14, 2017 - 10:25:42 PM
Last modification on : Thursday, February 7, 2019 - 2:29:56 PM
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Abdessamad Barbara, Abderrahim Jourani, Samuel Vaiter. Maximal Solutions of Sparse Analysis Regularization. Journal of Optimization Theory and Applications, Springer Verlag, 2018, pp.1-23. ⟨10.1007/s10957-018-1385-3⟩. ⟨hal-01467965⟩

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