Improved Complexity Analysis of Full Nesterov–Todd Step Interior-Point Methods for Semidefinite Optimization

G. Q. Wang (), Y. Q. Bai (), X. Y. Gao () and D. Z. Wang ()
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G. Q. Wang: Shanghai University of Engineering Science
Y. Q. Bai: Shanghai University
X. Y. Gao: Heilongjiang University
D. Z. Wang: Shanghai University of Engineering Science

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 1, No 12, 242-262

Abstract: Abstract In this paper, we present an improved convergence analysis of full Nesterov–Todd step feasible interior-point method for semidefinite optimization, and extend it to the infeasible case. This improvement due to a sharper quadratic convergence result, which generalizes a known result in linear optimization and leads to a slightly wider neighborhood for the iterates in the feasible algorithm and for the feasibility steps in the infeasible algorithm. For both versions of the full Nesterov–Todd step interior-point methods, we derive the same order of the iteration bounds as the ones obtained in linear optimization case.

Keywords: Interior-point methods; Semidefinite optimization; Small-update method; Polynomial complexity; 90C22; 90C51 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-014-0619-2

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