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Efficient and stable implementations of linear programming methods, both boundary and interior point, present many challenges, including sparsity preservation, stability and adaptations to special structures. Interior point methods appear to have an advantage over boundary methods for the first two, since the sparsity patterns are invariant during the iterations and the linear systems to be solved are symmetric and positive definite. Boundary methods have an advantage for special structures, since these methods can take advantage of the unimodularity of the underlying matrix A, and thus deal with integral and triangular systems, while interior point methods must necessarily work with a real positive definite and symmetric system of equations. It is not clear if this advantage will carry over when the underlying matrix is very large. Variants of the simplex method that are specialized for special structures are well developed, almost no effort has been given to interior point methods for such implementations.
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