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Implementation of Interior-Point Methods for LP Based on Krylov Subspace Iterative Solvers with Inner-Iteration Preconditioning
澳门新葡8455最新网站:2016年11月30日 13:39 点击数:

报告人:Ken Hayami

报告地点:澳门新葡8455最新网站104室

报告澳门新葡8455最新网站:2016年12月07日星期三13:30-14:30

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报告摘要:

We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe ill-conditioning of linear equations solved in the final phase of interior-point iterations. The employed Krylov subspace methods do not suffer from rank-deficiency and therefore no preprocessing is necessary even if rows of the constraint matrix are not linearly independent. Extensive numerical experiments are conducted over diverse instances of 125 LP problems including Netlib, QAPLIB, and Mittelmann’s collections. The number of variables of the largest problem is 434,580. It turns out that our implementation is more stable and robust than the standard public domain solvers SeDuMi (Self-Dual Minimization) and SDPT3 (Semidefinite Programming Toh-Todd-Tütüncü) without increasing CPU time. As far as we know, this is the first result that an interior-point method entirely based on iterative solvers succeed in solving a fairly large number of standard LP instances from benchmark libraries under the standard stopping criteria.

This is joint work with Ms.Yiran Cui, Dr. Keiichi Morikuni, and Prof.Takashi Tsuchiya

主讲人概况:

Ken Hayami obtained PhD from the Wessex Institute of Technology (1991) and the University of Tokyo (1993), respectively. Currently, he is a professor in the Principles of Informatics Research Division of NII and the Department of Informatics at SOKENDAI (The Graduate University of Advanced Studies) .

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