caa a22 4500 445839724 CHVBK 20180317145340.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00186-010-0334-1 doi (NATIONALLICENCE)springer-10.1007/s00186-010-0334-1 Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming [Elektronische Daten] [Jian Zhang, Kecun Zhang] In this paper, we propose a second order interior point algorithm for symmetric cone programming using a wide neighborhood of the central path. The convergence is shown for commutative class of search directions. The complexity bound is $${O(r^{3/2}\,\log\epsilon^{-1})}$$ for the NT methods, and $${O(r^{2}\,\log\epsilon^{-1})}$$ for the XS and SX methods, where r is the rank of the associated Euclidean Jordan algebra and $${\epsilon\,{ > }\,0}$$ is a given tolerance. If the staring point is strictly feasible, then the corresponding bounds can be reduced by a factor of r 3/4. The theory of Euclidean Jordan algebras is a basic tool in our analysis. Springer-Verlag, 2010 Linear programming nationallicence Symmetric cone nationallicence Euclidean Jordan algebra nationallicence Interior point method nationallicence Polynomial complexity nationallicence Zhang Jian Faculty of Science, Xi'an Jiaotong University, P.O.Box 2325, 710049, Xi'an, People's Republic of China aut Zhang Kecun Faculty of Science, Xi'an Jiaotong University, P.O.Box 2325, 710049, Xi'an, People's Republic of China aut Mathematical Methods of Operations Research Springer-Verlag 73/1(2011-02-01), 75-90 1432-2994 73:1<75 2011 73 186 https://doi.org/10.1007/s00186-010-0334-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-010-0334-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Jian Faculty of Science, Xi'an Jiaotong University, P.O.Box 2325, 710049, Xi'an, People's Republic of China aut NATIONALLICENCE 700 1- Zhang Kecun Faculty of Science, Xi'an Jiaotong University, P.O.Box 2325, 710049, Xi'an, People's Republic of China aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 73/1(2011-02-01), 75-90 1432-2994 73:1<75 2011 73 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer