一类线性规划逆问题及解法

本文讨论了逆ＬＰ问题的更一般的情况，这里称它为广义逆ＬＰ问题，即在知道了一部分变量和价值系数的条件下，求余下的未知的变量和价值系数，将它们合起来组成给定的ＬＰ问题的最优解。显然若知道全部价值系数就成为ＬＰ问题；若知道全部变量就成为逆ＬＰ问题，它是在根据研制应用软件时提出的。文中给出了解广义逆ＬＰ问题的算法，并成功地用于“宏观经济调控系统”等应用软件的研制中，对要解决的实际问题，给出了强多项式算法。

AN ALGORITHM FOR SOLVING SOMEINVERSE LINEAR PROGRAMMING PROBLEMS

In this paper an extended inverse LP problem was considered, in which oneneeds to find the resting unknown variable and cost Coefficients while partly variable andcost coefficients of the LP problem are given, so that they form an optimal one. An algorithmfor solving extended inver LP problem is suggested. The algorithm was successfully appliedto the National Control of Market Economy, for this special case it is strongly polynomialcomplexity.