We propose a variation of the pointwise residual method for solving primal and dual ill-posed linear programming with approximate data, sensitive to small perturbations. The method leads to an auxiliary problem, which is also a linear programming problem. Theorems of existence and convergence of approximate solutions are established and optimal estimates of approximation of initial problem solutions are achieved.

中文翻译：

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用近似数据求解原始和对偶病态线性规划问题的 POINTWISE 残差方法

我们提出了一种点状残差方法的变体，用于求解具有近似数据的原始和对偶病态线性规划，对小扰动敏感。该方法导致一个辅助问题，这也是一个线性规划问题。建立了近似解的存在性和收敛性定理，实现了初始问题解近似的最优估计。