Path-following interior point algorithms for the Cartesian P*(κ)-LCP over symmetric cones

Science in China, Series A: Mathematics

Volumn 52, Issue 8, 2009, Pages 1769-1784

  Luo, Zi Yan ^a   Xiu, Nai Hua ^a  

^a BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

Cartesian P*( ) property; Complexity; Global convergence; Path following interior point algorithm; Symmetric cone linear complementarity problem

Indexed keywords

EID: 70349987376     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-008-0174-0     Document Type: Article

References (23)

1. Faybusovich L. Euclidean Jordan algebras and interior-point algorithms. Positivity, 1: 331-357 (1997)
2. Faybusovich L. Linear systems in Jordan algebras and primal-dual interior-point algorithms. J Comput Appl Math, 86: 149-175 (1997)
3. Faybusovich L, Arana R. A long-step primal-dual algorithm for the symmetric programming problem. Technical Report, Department of Mathematics, Notre Dame University, 2000
4. Lu Y, Yuan Y. An interior-point trust region algorithm for general symmetric cone programming. SIAM J Optim, 18: 65-86 (2007)
5. Muramatsu M. On a commutative class of search directions for linear programming over symmetric cones. J Optim Theory Appl, 112: 595-625 (2002)
6. Rangarajan B K. Polynomial convergence of infeasible-interior-point methods over symmetric cones. SIAM J Optim, 16: 1221-1229 (2006)
7. Schmieta S H, Alizadeh F. Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones. Math Oper Res, 26: 543-564 (2001)
8. Schmieta S H, Alizadeh F. Extension of primal-dual interior point algorithm to symmetric cones. Math Program, 96: 409-438 (2003)
9. Andersen E D, Roos C, Terlaky T. On implementing a primal-dual interior-point method for conic quadratic optimization. Math Program, 95: 249-277 (2003)
10. Faybusovich L, Lu Y. Jordan-algebraic aspects of nonconvex optimization over symmetric cones. Appl Math Optim, 53: 67-77 (2006)
11. Lu Y, Yuan Y. An interior-point trust-region polynomial algorithm for convex quadratic minimization subject to convex constraints. Optim Methods Softw, 23: 251-258 (2008)
12. Yoshise A. Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones. SIAM J Optim, 17: 1129-1153 (2006)
13. Yoshise A. A homogeneous algorithm for complementarity problems over symmetric cones. Technical Report, Graduate School of Systems and Information Engineering University of Tsukuba, 2007
14. Chen X, Qi H D. Cartesian P-property and its applications to the semidefinite linear complementarity problem. Math Program, 106: 177-201 (2006)
15. Kong L C, Tuņcel, L., Xiu N H. Vector-valued implicit lagrangian for symmetric cone complementarity problems. Research Report CORR 2006-24, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 2006
16. Kojima M, Megiddo N, Noma T, et al. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. Lecture Notes in Computer Science, 538. Berlin: Springer-Verlag, 1991
17. Ji J, Potra F A. An infeasible-interior-point method for the P*-matrix LCP. Reports on Comput Math 52, Department of Mathematics, University of Iowa, Iowa City, IA, 1994
18. Ji J, Potra F A, Sheng R. A predictor-corrector method for the P*-matrix LCP from infeasible starting points. Optim Mehods Softw, 6: 109-126 (1995)
19. Miao J. A quadratically convergent O((κ+1) √ nL)-iteration algorithm for the P*(κ)-matrix linear complementarity problem Math Program, 69: 355-368 (1995)
20. Potra F A, Sheng R. Predictor-corrector algorithm for solving P*(κ)-matrix LCP from arbitrary positive starting points. Math Program, 76: 223-244 (1996)
21. Luo Z Y, Xiu N H. Solution existence and boundedness of symmetric cone linear complementarity problems with the Cartesian P*(κ)-property. Preprint, Department of Applied Mathematics, Beijing Jiaotong University, 2007
22. Koecher M. The Minnesota Notes on Jordan Algebra and Their Applications. Berlin: Springer, 1962
23. Faraut J, Koŕanyi A. Analysis on Symmetric Cones. New York: Oxford University Press, 1994