Abstract
We show that the problem of exiting a degenerate vertex is as hard as the general linear programming problem. More precisely, every linear programming problem can easily be reduced to one where the second best vertex (which is highly degenerate) is already given. So, to solve the latter, it is sufficient to exit that vertex in a direction that improves the objective function value.
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Megiddo, N. A note on degeneracy in linear programming. Mathematical Programming 35, 365–367 (1986). https://doi.org/10.1007/BF01580886
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DOI: https://doi.org/10.1007/BF01580886