A Quadratically Convergent O(sqrt{n}L)-Iteration Algorithm for Linear Programming

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dc.contributor.authorYe, Y.en_US
dc.contributor.authorGüller, O.en_US
dc.contributor.authorTapia, R.A.en_US
dc.contributor.authorZhang, Y.en_US
dc.date.accessioned2018-06-18T17:30:46Zen_US
dc.date.available2018-06-18T17:30:46Zen_US
dc.date.issued1991-08en_US
dc.date.noteAugust 1991en_US
dc.description.abstractRecently, Ye et al. proposed a large step modification of the Mizuno-Todd-Ye predictor-corrector interior-point algorithm for linear programming. They demonstrated that the large-step algorithm maintains theO (sqrt{n}L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.en_US
dc.format.extent18 ppen_US
dc.identifier.citationYe, Y., Güller, O., Tapia, R.A., et al.. "A Quadratically Convergent O(sqrt{n}L)-Iteration Algorithm for Linear Programming." (1991) <a href="https://hdl.handle.net/1911/101727">https://hdl.handle.net/1911/101727</a>.en_US
dc.identifier.digitalTR91-26en_US
dc.identifier.urihttps://hdl.handle.net/1911/101727en_US
dc.language.isoengen_US
dc.titleA Quadratically Convergent O(sqrt{n}L)-Iteration Algorithm for Linear Programmingen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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