The Four-Block Model Matching Problem in $l^1 $ and Infinite-Dimensional Linear Programming - Staffans, Olof J. (SIAM journal on control and optimization, 1993)
The purpose of this work is fourfold. First the reader is introduced to the present state of the theory behind the solution of the general model matching problem in $l^1 $. This solution is based on the fact that the model matching problem can be recast as an infinite-dimensional linear programming problem. However, the transformation into linear programming form is highly nonunique, which leads to the second question of discussion, namely, how to find a "good" linear programming formulation. It is shown that the presently available formulations contain some redundancies that limit the applicability of the theory and lead to linear programming systems containing unnecessary degeneracies. The third object of this work is to study problems related to the computational complexity of two different approximation methods for the solution of the infinite-dimensional linear programming systems. Both of these methods are needed in order to get two-sided error bounds on the cutoff error. One complication is that even after the extra redundancies that were mentioned above have been removed, there are certain multi-output problems that contain a massive intrinsic degeneracy. Finally, the convergence properties of the two solution schemes are investigated, and it is explained which properties of the original linear programming formulation are needed for different types of convergence.