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W Cook L Lovasz and A Schrijver A polynomialtime test for total
J Fonlupt and M Raco Orientation of matrices
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algorithm apply approximation assume b-KEG basis bipartite bipartite graph cocircuit column Combinatorial components condition cone constraints contains convex convex set Corollary corresponding cross-free cycle define denote digraph directed cuts Discrete Mathematics distributive lattice edge equation error exists extreme points feasible set feasible solution finite flow problem follows Gaussian elimination given graph G Hence inequalities iteration Lemma linear program lower bound Mathematical Programming matrix matroid maximum minimal minimum MlP-representable multiplier sets network flow node nondegeneracy nondegenerate nonempty nonlinear programming nonnegative nonzero element objective function obtain Operations Research optimal solution paper partition path polyhedra polyhedron polymatroid polynomial polytope proof of Theorem Proposition prove quasi-Newton methods recession directions representation satisfying Section simplex algorithm simplex method solve submodular flow submodular function submodular system subset supermodular Suppose T-join Theorem Theorem 2.1 totally dual integral unique upper bound vertex vertices x'-tight