On the probabilistic complexity of finding an approximate solution for linear programming

We consider the problem of finding an @e-optimal solution of a standard linear program with real data, i.e., of finding a feasible point at which the objective function value differs by at most @e from the optimal value. In the worst-case scenario the best complexity result to date guarantees that such a point is obtained in at most O(n|ln@e|) steps of an interior-point method. We show that the expected value of the number of steps required to obtain an @e-optimal solution for a probabilistic linear programming model is at most O(min{n^1^.^5,mnln(n)})+log"2(|ln@e|).