Application of a Class of Preconditioners to Large Scale Linear Programming Problems
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Date
1999
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
In most interior point methods for linear programming, a
sequence of weighted linear least squares problems are solved, where the
only changes from one iteration to the next are the weights and the right
hand side. The weighted least squares problems are usually solved as
weighted normal equations by the direct method of Cholesky factorization. In this paper, we consider solving the weighted normal equations
by a preconditioned conjugate gradient method at every other iteration.
We use a class of preconditioners based on a low rank correction to a
Cholesky factorization obtained from the previous iteration. Numerical
results show that when properly implemented, the approach of combining
direct and iterative methods is promising
Description
Keywords
Weighted linear least squares, Parallel processing, Preconditioners, Linear programming, Primal-dual infeasible interior point algorithms
Citation
Baryamureeba, V., & Steihaug, T. (1999, August). Application of a class of preconditioners to large scale linear programming problems. In European Conference on Parallel Processing (pp. 1044-1048). Springer, Berlin, Heidelberg.