The four-block model matching problem in l1

The formulation of the l¹ minimization problem as an infinite-dimensional linear programming problem is discussed, along with some aspects of the solution process. Two methods are applied simultaneously making it possible to get both upper bounds and lower bounds on the true optimum, and to compute the optimum of the full problem to within any given tolerance. How to determine the size of a truncated problem is considered. The convergence of the optima of the truncated problems to the true optimum is discussed, along with the questions of whether the full solutions of the truncated primal problems converge to a full solution of the original primal problem, and whether the full solutions of the truncated dual problems tend to a full solution of the original dual problem