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A New Second-Order Mehrotra-Type Predictor-Corrector Algorithm for SDO

A New Second-Order Mehrotra-Type Predictor-Corrector Algorithm for SDO
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摘要 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 direction.In 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 iterates.It 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. 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 direction.In 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 iterates.It 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.
出处 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2016年第2期99-109,共11页 武汉大学学报(自然科学英文版)
基金 Supported by the National Natural Science Foundation of China(71471102)
关键词 Mehrotra-type algorithm predictor-corrector methods semidefinite optimization Mehrotra-type algorithm predictor-corrector methods semidefinite optimization
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