Network Flows and Monotropic OptimizationDescribes optimization problem in which duality is an important computational tool, including network and linear programming. Introduces monotropic programming, a new form of mathematical programming developed by the author. |
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applied arbitrary arcs assignment associated basis called capacity Chapter circuit circulation closed column compatible condition connected constraints constructed convex corresponding cost course defined described determined direction distribution algorithm dual duality elementary elements equivalent Example Exercise existence expressed extreme fact feasible distribution feasible solution Figure finite flux formula function given initial integral intervals iteration latter least linear programming matrix max flow maximal minimizing node Note obtained optimal differential problem optimal distribution problem optimal solution out-of-kilter painted pair particular path piecewise linear pivoting positive possible potential primal procedure proof Prove reduces relation relative replaced representation represented respect routing satisfying sense sequence Show simplex method solving span step subroutine Suppose tableau tension terminate theorem theorem in Section theory tree Tucker values vector whereas