Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-new-infeasible-interior-point-algorithm-for-linear-programming-over-S00sccci4I
References (22)
-
G. Gu, M. Zangiabadi, Kees Roos (2011)
Full Nesterov-Todd step infeasible interior-point method for symmetric optimizationEur. J. Oper. Res., 214
-
L. Faybusovich (1997)
Euclidean Jordan Algebras and Interior-point AlgorithmsPositivity, 1
-
B. Rangarajan (2006)
Polynomial Convergence of Infeasible-Interior-Point Methods over Symmetric ConesSIAM J. Optim., 16
-
Y. Nesterov, M. Todd (1998)
Primal-Dual Interior-Point Methods for Self-Scaled ConesSIAM J. Optim., 8
-
F. Alizadeh, Yu Xia (2011)
The Q Method for Symmetric Cone ProgrammingJournal of Optimization Theory and Applications, 149
-
L. Faybusovich (1997)
Linear systems in Jordan algebras and primal-dual interior-point algorithmsJournal of Computational and Applied Mathematics, 86
-
M. Frei (2016)
Analysis On Symmetric Cones -
Guo-Qiang Wang, Yanqin Bai (2012)
A New Full Nesterov–Todd Step Primal–Dual Path-Following Interior-Point Algorithm for Symmetric OptimizationJournal of Optimization Theory and Applications, 154
-
Jian Zhang, Kecun Zhang (2011)
Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programmingMathematical Methods of Operations Research, 73
-
Yang Li, T. Terlaky (2010)
A New Class of Large Neighborhood Path-Following Interior Point Algorithms for Semidefinite Optimization with O(√n log (Tr(X0S0)/ε)) Iteration ComplexitySIAM J. Optim., 20
-
S. Schmieta, F. Alizadeh (2003)
Extension of primal-dual interior point algorithms to symmetric conesMathematical Programming, 96
-
Y. Nesterov, M. Todd (1997)
Self-Scaled Barriers and Interior-Point Methods for Convex ProgrammingMath. Oper. Res., 22
-
Hongwei Liu, Ximei Yang, Changhe Liu (2013)
A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone ProgrammingJournal of Optimization Theory and Applications, 158
-
Wenbao Ai, Shuzhong Zhang (2005)
An O(\sqrtn L) Iteration Primal-dual Path-following Method, Based on Wide Neighborhoods and Large Updates, for Monotone LCPSIAM J. Optim., 16
-
Wenbao Ai (2004)
Neighborhood-following algorithms for linear programmingScience in China Series A: Mathematics, 47
-
W. Ai, S. Zhang (2005)
An $$O\left( {\sqrt n L} \right)$$ O ( n L ) iteration primal-dual path-following method, based on wide neighborhoods and large updates, for monotone LCPSIAM J. Optim., 16
-
R. Monteiro, Yin Zhang (1998)
A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programmingMathematical Programming, 81
-
F. Potra (2009)
An Infeasible Interior Point Method for Linear Complementarity Problems over Symmetric Cones, 1168
-
Li Changhe, L. Hongwei, Shang Youlin (2013)
Neighborhood-following algorithms for symmetric cone programming, 43
-
Y. Li, T. Terlaky (2010)
A new class of large neighborhood path-following interior point algorithms for semidefinite optimization with $$O\left( {\sqrt n \log \frac{{Tr\left( {{X^0}{S^0}} \right)}}{\varepsilon }} \right)$$ O ( n log T r ( X 0 S 0 ) ε ) iteration complexitySIAM J. Optim., 20
-
Osman Güler (1996)
Barrier Functions in Interior Point MethodsMath. Oper. Res., 21
-
Y. Nesterov, A. Nemirovski (1994)
Interior-point polynomial algorithms in convex programming, 13
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-017-0697-7
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we present an infeasible-interior-point algorithm, based on a new wide neighbourhood N(τ 1, τ 2, η), for linear programming over symmetric cones. We treat the classical Newton direction as the sum of two other directions. We prove that if these two directions are equipped with different and appropriate step sizes, then the new algorithm has a polynomial convergence for the commutative class of search directions. In particular, the complexity bound is O(r 1.5logε −1) for the Nesterov-Todd (NT) direction, and O(r 2logε −1) for the xs and sx directions, where r is the rank of the associated Euclidean Jordan algebra and ε > 0 is the required precision. If starting with a feasible point (x 0, y 0, s 0) in N(τ 1, τ 2, η), the complexity bound is $$O\left( {\sqrt r \log {\varepsilon ^{ - 1}}} \right)$$ O ( r log ε − 1 ) for the NT direction, and O(rlogε −1) for the xs and sx directions. When the NT search direction is used, we get the best complexity bound of wide neighborhood interior-point algorithm for linear programming over symmetric cones.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Aug 7, 2017