Complexity analysis of an interior point algorithm for the semidefinite optimization based on a kernel function with a double barrier term
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| 008 | 210128e20150301xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-1314-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-1314-4 | ||
| 100 | 1 | |a Achache |D Mohamed |u Laboratoire de Mathématiques Fondamentales et Numériques, Faculté des Sciences, Université Ferhat Abbas Sétif 1, Sétif, Algérie |4 aut | |
| 245 | 1 | 0 | |a Complexity analysis of an interior point algorithm for the semidefinite optimization based on a kernel function with a double barrier term |h [Elektronische Daten] |c [Mohamed Achache] |
| 520 | 3 | |a 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. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Semidefinite optimization |2 nationallicence | |
| 690 | 7 | |a kernel functions |2 nationallicence | |
| 690 | 7 | |a primal-dual interior point methods |2 nationallicence | |
| 690 | 7 | |a large and small-update algorithms |2 nationallicence | |
| 690 | 7 | |a complexity of algorithms |2 nationallicence | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/3(2015-03-01), 543-556 |x 1439-8516 |q 31:3<543 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-1314-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-1314-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Achache |D Mohamed |u Laboratoire de Mathématiques Fondamentales et Numériques, Faculté des Sciences, Université Ferhat Abbas Sétif 1, Sétif, Algérie |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/3(2015-03-01), 543-556 |x 1439-8516 |q 31:3<543 |1 2015 |2 31 |o 10114 | ||