A simple polynomial-time rescaling algorithm for solving linear programs

Authors:
John Dunagan;Santosh Vempala_aff2n3
Affiliations:
One Microsoft Way, Microsoft Research, 98052, Redmond, WA, USA;af2 Massachusetts Institute of Technology, Department of Mathematics, 02139, Cambridge, MA, USA and af3 Georgia Tech, College of Computing, 801 Atlantic Drive, Atlanta, GA, 30332, USA
Venue:
Mathematical Programming: Series A and B
Year:
2008

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Abstract

The perceptron algorithm, developed mainly in the machine learning literature, is a simple greedy method for finding a feasible solution to a linear program (alternatively, for learning a threshold function). In spite of its exponential worst-case complexity, it is often quite useful, in part due to its noise-tolerance and also its overall simplicity. In this paper, we show that a randomized version of the perceptron algorithm along with periodic rescaling runs in polynomial-time. The resulting algorithm for linear programming has an elementary description and analysis.