caa a22 4500 605461597 CHVBK 20210128100244.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10114-015-1314-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-1314-4 Achache Mohamed Laboratoire de Mathématiques Fondamentales et Numériques, Faculté des Sciences, Université Ferhat Abbas Sétif 1, Sétif, Algérie aut Complexity analysis of an interior point algorithm for the semidefinite optimization based on a kernel function with a double barrier term [Elektronische Daten] [Mohamed Achache] In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization (SDO) problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barrier term. With this function we define a new search direction and also a new proximity function for analyzing its complexity. We show that if q 1 > q 2 > 1, the algorithm has $O((q_1 + 1)n^{\frac{{q_1 + 1}} {{2(q_1 - q_2 )}}} \log \tfrac{n} {e}) $ and $O((q_1 + 1)^{\frac{{3q_1 - 2q_2 + 1}} {{2(q_1 - q_2 )}}} \sqrt n \log \tfrac{n} {e}) $ complexity results for large- and small-update methods, respectively. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Semidefinite optimization nationallicence kernel functions nationallicence primal-dual interior point methods nationallicence large and small-update algorithms nationallicence complexity of algorithms nationallicence Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/3(2015-03-01), 543-556 1439-8516 31:3<543 2015 31 10114 https://doi.org/10.1007/s10114-015-1314-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-1314-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Achache Mohamed Laboratoire de Mathématiques Fondamentales et Numériques, Faculté des Sciences, Université Ferhat Abbas Sétif 1, Sétif, Algérie aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/3(2015-03-01), 543-556 1439-8516 31:3<543 2015 31 10114