On the Average Condition of Random Linear Programs

We give an ${\cal O}(\log n)$ bound for the expectation of the logarithm of the condition number ${\cal K}(A,b,c)$ introduced in “Solving Linear Programs with Finite Precision: I. Condition Numbers and Random Programs” [Math. Program., 99 (2004), pp. 175--196]. This bound improves the previously existing bound, which was of ${\cal O}(n)$, and yields average-case bounds for both the required precision and the complexity of computing an optimal basis (or a pair of primal-dual optimizers).

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