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dc.contributor.authorMousavi, Seyedahmad
dc.contributor.authorShen, Jinglai
dc.date.accessioned2019-04-17T19:07:49Z
dc.date.available2019-04-17T19:07:49Z
dc.date.issued2017-11-16
dc.description.abstractIn this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained ℓ1 recovery problems arising from sparse optimization, such as basis pursuit, LASSO, and basis pursuit denoising, as well as polyhedral gauge recovery. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of ℓ1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions. The results obtained in this paper not only recover the known solution uniqueness conditions in the literature by removing restrictive assumptions but also yield new uniqueness conditions for much broader constrained ℓ1-minimization problems.en_US
dc.description.urihttps://arxiv.org/abs/1711.05882en_US
dc.format.extent27 pagesen_US
dc.genrejournal articles preprintsen_US
dc.identifierdoi:10.13016/m2evju-hykh
dc.identifier.citationSeyedahmad Mousavi, Jinglai Shen , Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained ℓ 1 Minimization, Mathematics, Optimization and Control, 2017, https://arxiv.org/abs/1711.05882en_US
dc.identifier.urihttp://hdl.handle.net/11603/13449
dc.language.isoen_USen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subjectpolyhedral gauge recoveryen_US
dc.subjectconvex piecewise affine functionsen_US
dc.subjectLASSOen_US
dc.subjectℓ1 minimization problemsen_US
dc.titleSolution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained ℓ 1 Minimizationen_US
dc.typeTexten_US


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