Necessary and Sufficient Conditions of Solution Uniqueness in l(sub 1) Minimization (Preprint).

摘要

This paper shows that the solutions to various convex l(sub 1) minimization problems are unique if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other l(sub 1) models that either minimize f(Ax-b) or impose the constraint f(Ax-b).