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Splitting dense columns of constraint matrix in interior point methods for large scale linear programming. (English) Zbl 0814.65056
Summary: A method is proposed for handling dense columns of the constraint matrix of large scale linear programming problems. Such columns are known to create dense windows in the matrices \(AA^ T\) which are inverted at every iteration of the interior point method. Consequently, the Cholesky factor of \(AA^ T\) becomes dense, which degrades the efficiency of the \(LP\) code. In the method considered, all dense columns are then split into shorter ones. One dense \(AA^ T\) window of large size is thus replaced with \(p\) windows each of size \(p\) times smaller, leading to a remarkable reduction of the number of nonzeros in the matrix to be inverted and in its Cholesky factor.

MSC:
65K05 Numerical mathematical programming methods
90C05 Linear programming
65F05 Direct numerical methods for linear systems and matrix inversion
90C06 Large-scale problems in mathematical programming
Software:
symrcm
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References:
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