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Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 445–463 | Cite as

Simplified full Nesterov–Todd step infeasible interior-point algorithm for semidefinite optimization based on a kernel function

  • Weiwei WangEmail author
  • Hongwei Liu
  • Hongmei Bi
Original Research
  • 60 Downloads

Abstract

In this paper, we propose a new complexity analysis of the full Nesterov–Todd step infeasible interior-point algorithm for semidefinite optimization. With a specific feasibility step and the centering step induced by a well-known kernel function, the property of exponential convexity of the kernel function underlying the matrix barrier function is crucial in the analysis and enable us easily to estimate the proximity of iterates to center path. The analysis of the algorithm is simplified and the iteration bound obtained coincides with the currently best iteration bound for infeasible interior-point algorithm.

Keywords

Semidefinite optimization Infeasible interior-point algorithm Full Nesterov–Todd step Kernel function Exponential convexity 

Mathematics Subject Classification

90C51 90C22 

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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of ScienceXi’an Technological UniversityXi’anChina
  3. 3.School of ScienceAir Force Engineering UniversityXi’anChina

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