Technical Note—A Note on Reinverting the Dantzig-Wolfe Type Decomposed LP Basis

William J. Reich
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William J. Reich: Falstaff Brewing Corporation, St. Louis, Missouri

Operations Research, 1973, vol. 21, issue 1, 374-376

Abstract: This note reports an efficient routine that has been developed and successfully applied to the reinversion of decomposed LP bases of the Dantzig-Wolfe type. In sum, if r is the total number of subproblems in the original LP problem and k is the number of subproblem vectors in the decomposed basis, then only k − r Gauss-Jordan iterations are needed to invert the decomposed basis. The larger r , the more efficient and accurate the routine. This reduction in the number of Gauss-Jordan iterations is accomplished by finding the inverse of the wrong basis rapidly, and then making the necessary corrections to get the inverse of the right basis.

Date: 1973
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