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A SECOND ORDER mehrotra-type PREDICTOR-CORRECTOR algorithm FOR SEMIDEFINITE OPTIMIZATION

Journal of Systems Science & Complexity 2012年第6期25卷 1108-1121页

作者： Mingwang ZHANG College of Science China Three Gorges University

Abstract mehrotra-type predictor-corrector algorithm is one of the most effective primal-dual interior- point methods. This paper presents an extension of the recent variant of second order mehrotra-type predictor-corrector algorithm that was proposed by Salahi, et a1.（2006） for linear optimization. Basedon the NT direction as Newton search direction, it is shown that the iteration-complexity bound of thealgorithm for semidefinite optimization is which is similar to that of the correspondingalgorithm for linear optimization.

关键词： mehrotra-type algorithm polynomial complexity predictor-corrector algorithm semidef-inite optimization.

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A New Second-Order mehrotra-type Predictor-Corrector algorithm for SDO

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Wuhan University Journal of Natural Sciences 2016年第2期21卷 99-109页

作者： HUANG Fangyan ZHANG Mingwang HUANG Zhengwei College of Science China Three Gorges University College of Economics and Management China Three Gorges University

In Zhang’s recent works,a second-order mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had3/2 0 T 0O（nlog（X）gS/e）iteration complexity based on the NT direction as Newton search *** this paper,we extend the second-order mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new *** is proved that the iteration complexity is reduced to0 0O（nlog XgS/e）,which coincides with the currently best iteration bound of mehrotra-type predictor-corrector algorithm for semidefinite optimization.

关键词： mehrotra-type algorithm predictor-corrector methods semidefinite optimization

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维普期刊数据库

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Polynomial Complexity Bounds of mehrotra-type Predictor-corrector algorithms for Linear Programming over Symmetric Cones

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Chinese Quarterly Journal of Mathematics 2015年第4期30卷 475-494页

作者：刘长河尚有林李振国 School of Mathematics and Statistics Henan University of Science and Technology

We establish polynomial complexity corrector algorithms for linear programming over bounds of the mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.

关键词： linear programming symmetric cone Euclidean Jordan algebra interior-point methods mehrotra-type algorithm polynomial complexity

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