On the quadratic convergence of the simplified Mizuno-Todd-Ye algorithm for linear programming

SIAM Journal on Optimization

Volumn 7, Issue 1, 1997, Pages 66-85

  Gonzaga, Clovis I S C ^a   Tapia, Richard A ^b  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b RICE UNIVERSITY   (United States)

Author keywords

Linear programming; Predictor corrector algorithm; Primal dual interior point algorithm; Quadratic convergence

Indexed keywords

EID: 0031541267     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623493243569     Document Type: Article

References (20)

1. I. ADLER AND R. D. C. MONTEIRO, Limiting behavior of the affine scaling continuous trajcetories for linear programming problems, Math. Programming, 50 (1991), pp. 29-51.
2. C. GONZAGA, Path following algorithms for linear programming, SIAM Rev., 34 (1992), pp. 167-224.
3. C. GONZAGA AND R. A. TAPIA, On the Convergence of the Mizumo- Todd-Ye Algorithm to the Analytic Center of the Solution Set, Technical report TR92-41, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1992.
4. M. KOJIMA, S. MIZUNO, AND A. YOSHISE, A primal-dual interior-point method for linear programming, in Progress in Mathematical Programming, Interior-point and Related Methods, Nimrod Megiddo, ed., Springer-Verlag, Berlin, New York, 1989, pp. 29-47.
5. M. KOJIMA, S. MIZUNO, AND A. YOSHISE, An O(√nL) iteration potential reduction algorithm for linear complementarity problems, Math. Programming, 90 (1991), pp. 331-342.
6. I. J. LUSTIG, R. E. MARSTEN, AND D. F. SHANNO, Computational experience with a primal-dual interior-point method for linear programming, Linear Algebra Appl., 152 (1991), pp. 191-222.
7. K. MCSHANE, Superlinearly convergent O(√nL)-iteration interior-point algorithm for linear programming and the monotone linear complementarity problem, SIAM J. Optim., 4 (1994), pp. 247-261.
8. N. MEGIDDO, Pathways to the optimal set in linear programming, in Progress in Mathematical Programming, Interior-point and Related Methods, Nimrod Megiddo, ed., Springer-Verlag, Berlin, New York, 1989, pp. 131-158.
9. N. MEGIDDO AND M. SHUB, Boundary behaviour of interior point algorithms in linear programming, Math. Oper. Res., 14 (1989), pp. 97-146.
10. S. MEHROTRA, Quadratic, convergence in a primal-dual method, Math. Oper. Res., 18 (1993), pp. 741-751.
11. S. MIZUNO, M. J. TODD, AND Y. YE, On adaptive-step primal-dual interior-point algorithms for linear programming, Math. Oper. Res., 18 (1993), pp. 964-981.
12. R. C. MONTERIO AND I. ADLER, Interior path-following primal-dual algorithm. Part I: Linear programming, Math. Programming, 44 (1989), pp. 27-41.
13. R. A. TAPIA, Y. ZHANG, AND Y. YE, On the convergence of the iteration sequence in primal-dual interior point methods, Math. Programming, 68 (1995), pp. 141-154.
14. M. J. TODD AND Y. YE, A centered projective algorithm for linear programming, Math. Oper. Res., 15 (1990), pp. 508-529.
15. Y. YE, On the Q-order of convergence of interior-point algorithms for linear programming, in Proc. 1992 Symposium on Applied Mathematics, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China, 1992. pp. 534-543.
16. Y. YE, O. GÜLER, R. A. TAPIA, AND Y. ZHANG, A quadratically convergent O(√nL)-iteration algorithm for linear prograrmning, Math. Programming, 59 (1993), pp. 151-162
17. Y. YE, R. A. TAPIA, AND Y. ZHANG, A Superlinearly Convergent O( √nL)-Iteration Algorithm for Linear Programming, Technical report TR91-22, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1991.
18. Y. ZHANG AND R. A. TAPIA, A superlinearly convergent polynomial primal-dual interior-point algorithm for linear programming, SIAM J. Optim., 3 (1993), pp. 118-133.
19. Y. ZHANG AND R. A. TAPIA, Superlinear and quadratic convergence of primal-dual interior-point methods, for linear programming revisited, J. Optim. Theory Appl., 73 (1992), pp. 229-242.
20. Y. ZHANG, R. A. TAPIA, AND J. E. DENNIS, On the superlinear and quadratic convergence of primal-dual, interior-point linear programming algorithms, SIAM J. Optim., 2 (1992), pp. 304-324.