Ill-conditionedness and Interior-point Methods
نویسندگان
چکیده
As it is well-known, since the discovery of the interior-point methods linear programming (LP) is no longer synonymous with the celebrated simplex method. The interior-point methods (IPMs) have not only a better complexity bound than the simplex method (polynomial vs. exponential) but also enjoy practical efficiency and can be considerably faster than the simplex method for many (but not for all) large scale problems. It is the purpose of this paper to demonstrate that in the case of degeneracy, the interoir-point methods can be seriously affected by illconditioning, even in their most robust implementations, such as PCx [5], HOPDM [2], etc. For the detailed description and discussion of various IPMs see e.g. [1], [2], [4], [5]. In order to fix some notation, let us consider the following linear programming problem
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