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Nested-Decomposition Approach for Solving Staircase Linear Programs

机译：求解楼梯线性规划的嵌套分解方法

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The Nested Decomposition Principle of Manne and Ho is applied to the dual of a T-period staircase linear program, generating a sequence of one-period problems. These problems are coordinated only through communication of price and activity information between adjacent periods; an optimal coordination is achieved after repeated solution of the individual problems. The duals of the one-period problems reflect more naturally the structure of the primal problem. In this setting, a modified algorithm is developed which accelerates convergence by parametrizing the information exchanged between periods. Typically, information is provided to period t from previous and subsequent periods in the form of surrogate columns and modified right-hand side, and surrogate rows and modified cost coefficients, respectively. This algorithm may be implemented either by using existing linear programming software to solve the one-period problems, or through the use of data structures specifically adapted to this approach. Update formulas for such data structures are given and computational strategies which further accelerate convergence are discussed. (ERA citation 08:043123)

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