| 摘要 |
A method for optimizing the payoff at an industrial process characterized by n linear constraints and d real variables has a worst-case time complexity O(n3d2). The method involves the steps of (1) defining a plurality of constraint equations, each said constraint equation comprising a functional linear inequality of the process variables, one of the constraint equations comprising an objective function defining a payoff of the industrial process; (2) optimizing the payoff by (a) defining a multi-dimensional solution space from an intersection of hyperplanes defined by the constraint equations, the solution space having vertices each corresponding to a solution defined by a respective basis of the constraint equations; and (b) descending between peak ones of the vertic es in accordance with at least one pivoting rule, each said peak vertex defining an optimum for the payoff from the constraint equations of the respective basis, the pivoting rules comprise traversing th e peak vertices until a minimum one of the peak vertices is reached; and (3) implementing the industrial process in accordance with the solution defined by the minimum peak vertex.
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