Titlebook: Linear Programming Computation; Ping-Qi PAN Book 20141st edition Springer-Verlag Berlin Heidelberg 2014 deficient-basis method.duality.fac

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Dual Simplex Phase-l MethodThe mission of a dual Phase-I procedure is to provide an initial dual feasible simplex tableau (or basis) to the dual simplex method.

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D-Reduced Simplex MethodConsider the so-called “D-reduced problem” (25.3), i.e., . The associated dual problem is of an objective function involving a single variable. A so-called “D-reduced simplex method” will be developed to solve the preceding problem.

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Duality Principle and Dual Simplex Methodtly (except for the self-duality, see below). The former is referred to as . while the latter as .. It is important that there exists a close relationship between their feasible regions, optimal solutions and optimal values. The duality together with optimality conditions, yielding from it, constitu

Projection

Implementation of the Simplex Methodput to practical use via programming directly. Softwares, resulting by following the algorithms, step by step naively, would only solve textbook instances, involving only few variables and constraints, not real-world problems, especially large-scale sparse problems. Experiences indicate that impleme