Final iterations in interior point methods – preconditioned conjugate gradients and modified search directions
2000 ◽
Vol 41
(3)
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pp. 312-328
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Keyword(s):
AbstractIn this article we consider modified search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modified search directions are computed by solving perturbed systems in which the systems may be solved efficiently by the preconditioned conjugate gradient solver. A variation of Cholesky factorization is presented for computing a better preconditioner when the normal equations are ill-conditioned. These ideas have been implemented successfully and the numerical results show that the algorithms enhance the performance of the preconditioned conjugate gradients-based interior point methods.
2004 ◽
Vol 103
(1)
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pp. 153-179
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2018 ◽
Vol 13
(01)
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pp. 2050014
1999 ◽
Vol 11
(1-4)
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pp. 1-46
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Keyword(s):
1996 ◽
Vol 31
(4-5)
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pp. 49-54
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2000 ◽
Vol 11
(1)
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pp. 223-242
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Keyword(s):
2005 ◽
Vol 50
(7)
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pp. 1157-1166
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2010 ◽
Vol 25
(2)
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pp. 321-332
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Keyword(s):