For linear programs, we consider schemes for the formation of a generalized central path, which arise under the simultaneous use of interior and exterior penalty terms in the traditional Lagrange function and the minimax problems generated by it. The advantage of the new schemes is that they do not require a priori knowledge of feasible interior points in the primal or dual problem. Moreover, when applied to problems with inconsistent constraints, the schemes automatically lead to some of their generalized solutions, which have an important applied content. Descriptions of the algorithms, their justification, and results of numerical experiments are presented.

中文翻译：

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适用于不正确线性程序的内点方法

对于线性程序，我们考虑用于形成广义中心路径的方案，该方案是在传统拉格朗日函数中同时使用内部和外部惩罚项以及由此产生的极大极小问题而产生的。新方案的优点在于，它们不需要先验知识就可以解决原始问题或对偶问题中的可行内部点。而且，当应用于约束不一致的问题时，这些方案会自动导致其某些广义解决方案，这些解决方案具有重要的应用内容。给出了算法的说明，其合理性以及数值实验的结果。