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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.

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
Full Text: DOI
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