Author:
Cai Xinzhong,Wu Lin,Yue Yujing,Li Minmin,Wang Guoqiang
Abstract
Abstract
In this paper, we give a unified computational scheme for the complexity analysis of kernel-function-based primal-dual interior-point methods for convex quadratic optimization over symmetric cone. By using Euclidean Jordan algebras, the currently best-known iteration bounds for large- and small-update methods are derived, namely,
O
(
r
log
r
log
r
ε
)
and
O
(
r
log
r
ε
)
, respectively. Furthermore, this unifies the analysis for a wide class of conic optimization problems.
MSC:90C25, 90C51.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference42 articles.
1. Roos C, Terlaky T, Vial JP: Theory and Algorithms for Linear Optimization. An Interior-Point Approach. Wiley, Chichester; 1997.
2. Wright SJ: Primal-Dual Interior-Point Methods. SIAM, Philadelphia; 1997.
3. Ye Y: Interior Point Algorithms: Theory and Analysis. Wiley, Chichester; 1997.
4. Anjos MF, Lasserre JB International Series in Operational Research and Management Science 166. In Handbook on Semidefinite, Conic and Polynomial Optimization: Theory, Algorithms, Software and Applications. Springer, New York; 2012.
5. Peng J, Roos C, Terlaky T: Self-regular functions and new search directions for linear and semidefinite optimization. Math. Program. 2002,93(1):129–171. 10.1007/s101070200296
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