Linear programming; Integer programming graphs; Enumeration methods; Cutting plane methods; The knapsack problem; Integer programming over cones; The set covering and partitioning problems; Approximate methods; Integer nonlinear programming; Computational experience.
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Integer Programming and Graphs
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algorithm of Section assignment problem augmenting path basic feasible solution basic solution basis matrix binary bound algorithm branch and bound calculations choose coefficients composite cut computational Consider convex hull deleted directed graph dual simplex iteration edges element entering variable enumeration algorithm example Exercise exists extreme point fathomed fo.o go to Step Gomory graph group knapsack problem ILP's ILPC implicit enumeration implies incidence matrix integer forms integer programming integer solution linear programming max x0 maximum matching method of integer MILP nonnegative Note objective function obtained odd cycle optimal solution partition primal feasible recursion return to Step satisfies Set Covering Problem shortest path shown in Figure simplex algorithm slack variable Smith Normal Form Solve the LP source row surrogate constraint tableau Theorem totally unimodular traveling salesman problem upper bound vertex vertices yields