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**:** 59
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**:** 2016
**:** . . / . 59. .: , 2016. .23-44.

** :** ,

** (.):** interior point method, linear programming

**:** , . . . . .

** (.):** The interior point algorithm for a linear programming problem is considered. This algorithm consists of two stages. On the first stage we enter to the region of feasible solutions given the specified constraints. The second stage is optimization over the feasible region. The entering into the feasible region is represented as an extended linear programming problem by adding only one new variable. The main goal of the paper is to provide a theoretical justification of the process of entering into the feasible region under assumption of non-degeneracy of the extended problem.

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