A Superlinearly Convergent Polynomial Primal-Dual Interior-Point Algorithm for Linear Programming

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dc.contributor.authorZhang, Yin
dc.contributor.authorTapia, Richard
dc.date.accessioned2018-06-18T17:30:12Z
dc.date.available2018-06-18T17:30:12Z
dc.date.issued1991-02
dc.date.noteFebruary 1991 (Revised December 1991)
dc.description.abstractThe choice of the centering (or barrier) parameter and the step length parameter are the fundamental issues in primal-dual interior-point algorithms for linear programming. Various choices for these two parameters have been proposed that lead to polynomial algorithms. Recently, Zhang, Tapia and Dennis gave conditions that these choices must satisfy in order to achieve quadratic or superlinear convergence. However, it has not been shown that these conditions for fast convergence are compatible with the choices that lead to polynomiality. It is worth noting that none of the existing polynomial algorithms satisfies these fast convergence requirements. This paper gives an affirmative answer to the question: can an algorithm be both polynomial and superlinearly convergent? We construct and analyze a "large step" algorithm that possesses both polynomiality and Q-superlinear convergence. For nondegenerate problems, the convergence rate is actually Q-quadratic.
dc.format.extent31 pp
dc.identifier.citationZhang, Yin and Tapia, Richard. "A Superlinearly Convergent Polynomial Primal-Dual Interior-Point Algorithm for Linear Programming." (1991) <a href="https://hdl.handle.net/1911/101704">https://hdl.handle.net/1911/101704</a>.
dc.identifier.digitalTR90-40
dc.identifier.urihttps://hdl.handle.net/1911/101704
dc.language.isoeng
dc.titleA Superlinearly Convergent Polynomial Primal-Dual Interior-Point Algorithm for Linear Programming
dc.typeTechnical report
dc.type.dcmiText
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