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Two linear programming algorithms for the linear discrete ₁ norm problem

Computational studies by several authors have indicated that linear programming is currently the most efficient procedure for obtaining L, norm estimates for a discrete linear problem. However, there are several linear programming algorithms, and the "best" approach may depend on the problem's structure (e.g., sparsity, triangularity, stability). In this paper we shall compare two published simplex algorithms, one referred to as primal and the other referred to as dual, and show that they are conceptually equivalent.