On the expected condition number of linear programming problems (Q1402168)

The authors examine the condition number \(C(A)\) introduced by \textit{D. Cheung} and \textit{F. Cucker} [Math. Program. 91A, No. 1, 163-174 (2001; Zbl 1072.90564)] for linear programming. It is assumed that the matrix coefficients are independent, identically distributed standard Gaussian random variables. The moments of \(C(A)\) are estimated. When \(n\) is sufficiently larger than \(m\), when \(A\) is \(m\times n\), then \(E(\ln(C(A))= \max\{\ln m,\ln\ln n\}+ O(1)\). Bounds of an alternative condition number are also estimated.