Skip to Main content Skip to Navigation
Journal articles

On the solution uniqueness characterization in the L1 norm and polyhedral gauge recovery

Abstract : This paper first proposes another proof of the necessary and sufficient conditions of solution uniqueness in 1-norm minimization given recently by H. Zhang, W. Yin, and L. Cheng. The analysis avoids the need of the surjectivity assumption made by these authors and should be mainly appealing by its short length (it can therefore be proposed to students exercising in convex optimization). In the second part of the paper, the previous existence and uniqueness characterization is extended to the recovery problem where the ℓ 1 norm is substituted by a polyhedral gauge. In addition to present interest for a number of practical problems, this extension clarifies the geometrical aspect of the previous uniqueness characterization. Numerical techniques are proposed to compute a solution to the polyhedral gauge recovery problem in polynomial time and to check its possible uniqueness by a simple linear algebra test.
Document type :
Journal articles
Complete list of metadata

Cited literature [39 references]  Display  Hide  Download
Contributor : Jean Charles Gilbert Connect in order to contact the contributor
Submitted on : Wednesday, August 10, 2016 - 10:19:41 AM
Last modification on : Friday, July 8, 2022 - 10:10:21 AM
Long-term archiving on: : Friday, November 11, 2016 - 10:56:03 AM


Files produced by the author(s)


Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives 4.0 International License




Jean Charles Gilbert. On the solution uniqueness characterization in the L1 norm and polyhedral gauge recovery. Journal of Optimization Theory and Applications, Springer Verlag, 2016, 1 (1), pp.1-32. ⟨10.1007/s10957-016-1004-0⟩. ⟨hal-01187012v2⟩



Record views


Files downloads