Convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming

Optimization Methods and Software

Volumn 11, Issue 1, 1999, Pages 141-182

  Tsuchiya, Takashi ^a  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; POLYNOMIALS;

INTERIOR-POINT METHODS; POLYNOMIAL-TIME ALGORITHMS; PRIMAL-DUAL PATH-FOLLOWING METHODS; SECOND-ORDER CONE PROGRAMMING (SOCP) PROBLEMS;

LINEAR PROGRAMMING;

EID: 0033293480     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556789908805750     Document Type: Article

References (28)

1. Adler, I. and Alizadeh, F. (1994). Primal-dual interior-point algorithms for convex quadratically constrained and semidefinite optimization problems, Manuscript, May. (Revised: August, 1995).
2. Alizadeh, F. (1997). Optimization over the Ice-cream cone, Talk given at the 16th International Symposium on Mathematical Programming, Lausanne, Switzerland, August 24-29.
3. Alizadeh, F., Haeberly, J.-P. and Overton, M. (1998). Primal-dual interior-point methods for semidefinite programming, convergence rates, stability and numerical results, SIAM Journal on Optimization, 8, 746-768.
4. Alizadeh, F. and Schmieta, S. (1997). Optimization with semidefinite, quadratic and linear constraints. Technical Report RRR 23-97, RUTCOR, Rutgers University, NJ, USA, November.
5. Ben-Tal, A. and Nemirovski, A. (1994). Potential reduction polynomial time methods for truss topology design, SIAM Journal on Optimization, 4, 596-612.
6. Faybusovich, L. (1995). Jordan algebras, symmetric cones and interior-point methods, Manuscript, Department of Mathematics, Notre Dame, IN, USA.
7. Faybusovich, L. (1997). Linear systems in Jordan algebras and primal-dual interior-point algorithms, Journal of Computational and Applied Mathematics, 87, 149-175.
8. Faybusovich, L. (1997). Euclidean Jordan algebras and interior-point algorithms, Positivity, 1, 331-357.
9. Faraut, J. and Koráyi, A. (1994). Analysis on Symmetric Cones. Oxford University Press, New York.
10. Helmberg, C., Rendl, F., Vanderbei, R. J. and Wolkowicz, H. (1996). An interior-point method for semidefinite programming, SIAM Journal on Optimization, 6, 342-361.
11. Jarre, F. (1990/91). On the convergence of the method of analytic centers when applied to convex quadratic programs, Mathematical Programming, 49, 341-359.
12. Jarre, F., Kočvara, M. and Zowe, J. (1998). Optimal truss topology design by interior-point methods, SIAM Journal on Optimization, 8, 1084-1107.
13. Kojima, M., Mizuno, S. and Yoshise, A. (1989). A primal-dual interior point algorithm for linear programming, In Progress in Mathematical Programming, Interior-point and Related Methods (ed. N. Megiddo), Springer-Verlag, New York. 29-47.
14. Kojima, M., Shindoh, S. and Hara, S. (1997). Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices, SIAM Journal on Optimization, 7, 86-125.
15. Lobo, M., Vandenberghe, L., Boyd, S. and Lebret, H. (1998). Applications of second-order cone programming, Linear Algebra and its Applications, 284, 193-228.
16. Mehrotra, S. and Sun, J. (1991). A method of analytic centers for quadratically constrained convex quadratic programs, SIAM Journal on Numerical Analysis, 28, 529-544.
17. Monteiro, R. D. C. (1997). Primal-dual path-following algorithms for semidefinite programming, SIAM Journal on Optimization, 7, 663-678.
18. Monteiro, R. D. C. and Tsuchiya, T. (1999). Polynomial convergence of a new family of primal-dual algorithms for semidefinite programming, SIAM Journal on Optimization, 9, 551-577.
19. Monteiro, R. D. C. and Takashi Tsuchiya (1998). Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-Family of directions, manuscript, May. The Institute of Statistical Mathematics, Tokyo, Japan.
20. Monteiro, R. D. C. and Zhang, Y. (1998). A unified analysis for a class of path-following primal-dual interior-point algorithms for semidefinite programming, Mathematical Programming, 81, 281-299.
21. Nemirovskii, A. and Scheinberg, K. (1996). Extension of Karmarkar's algorithm onto convex quadratically constrained quadratic problems, Mathematical Programming, 72, 273-289.
22. Nesterov, Yu. and Nemirovskii, A. (1994). Interior Point Polynomial Methods in Convex Programming, (SIAM Publications, Philadelphia, Pennsylvania, USA).
23. Nesterov, Y. E. and Todd, M. (1997). Self-scaled barriers and interior-point methods for convex programming, Mathematics of Operations Research, 22.
24. Nesterov, Y. E. and Todd, M. (1998). Primal-dual interior-point methods for self-scaled cones, SIAM Journal on Optimization, 8, 324-364.
25. Schmieta, S. and Alizadeh, F. (1998). Associative algebras, symmetric cones and polynomial time interior point algorithms, Technical Report RRR 17-98, RUTCOR, Rugters University, NJ, USA, June.
26. Todd, M. J. Toh, K. C. Tütüncü R. H. (1998). On the Nesterov-Todd direction in semidefinite programming, SIAM Journal on Optimization, 8, 769-796.
27. Tsuchiya, T. (1997). A polynomial primal-dual path-following algorithm for second-order cone programming. Research Memorandum No. 649, The Institute of Statistical Mathematics, Tokyo, Japan, October. (Revised: December 1997).
28. Xue, G. and Ye, Y. (1997). Efficient algorithms for minimizing a sum of Euclidean norms with applications, SIAM J. Optimization, 7, 1017-1036.