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

Authors:
Jun Ji;Florian A. Potra
Affiliations:
Department of Mathematics, Kennesaw State University, Kennesaw, GA 30144, USA;Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Venue:
Journal of Complexity
Year:
2008

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Abstract

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|).