Improved complexity using higher-order correctors for primal-dual Dikin affine scaling

Mathematical Programming, Series B

Volumn 76, Issue 1, 1997, Pages 117-130

  Jansen, B ^a   Roos, C ^a   Terlaky, T ^a   Ye, Y ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Affine scaling; Complexity; Interior point algorithm; Linear programming

Indexed keywords

EID: 0000705686     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02614380     Document Type: Article

References (21)

1. E.R. Barnes, "A variation on Karmarkar's algorithm for solving linear programming problems," Mathematical Programming 36 (1986) 174-182.
2. D.A. Bayer and J.C. Lagarias, "The nonlinear geometry of linear programming: I. Affine and projective scaling trajectories, II. Legendre transform coordinates and central trajectories," Transactions of the American Mathematical Society 314 (1989) 499-581.
3. I.I. Dikin, "Iterative solution of problems of linear and quadratic programming," Doklady Akademiia Nauk SSSR 174 (1967) 747-748.
4. 3 L) operations," in: N. Megiddo, ed., Progress in Mathematical Programming, Interior Point and Related Methods (Springer, New York, 1988) pp. 1-28.
5. P.-F. Hung and Y. Ye, "An asymptotical O(√n L)-iteration path-following linear programming algorithm that uses long steps," Working Paper, College of Business Administration, The University of Iowa, Iowa City, IA (1994).
6. B. Jansen, C. Roos, and T. Terlaky, "A polynomial primal-dual Dikin-type algorithm for linear programming," Mathematics of Operations Research 21 (1996) 341-353.
7. B. Jansen, C. Roos, and T. Terlaky, "A family of polynomial affine scaling algorithms for positive semi-definite linear complementarity problems," Technical Report 93-112, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands (1993).
8. M. Kojima, S. Mizuno, and A. Yoshise, "A primal-dual interior point algorithm for linear programming," in: N. Megiddo, ed., Progress in Mathematical Programming, Interior Point and Related Methods (Springer, New York, 1989) pp. 29-47.
9. M. Kojima, S. Mizuno, and A. Yoshise, "A polynomial-time algorithm for a class of linear complementarity problems," Mathematical Programming 44 (1989) 1-26.
10. I.J., Lustig, R.E. Marsten and D.F. Shanno, "Computational experience with a primal-dual interior point method for linear programming" Linear Algebra and its Applications 152 (1991) 191-222.
11. N. Megiddo, "Pathways to the optimal set in linear programming," in: N. Megiddo, ed., Progress in Mathematical Programming, Interior Point and Related Methods (Springer, New York, 1988) pp. 131-158.
12. S. Mehrotra, "On the implementation of a (primal-dual) interior point method," SIAM Journal on Optimization 2 (1992) 575-601.
13. R.C. Monteiro and I. Adler, "Interior path following primal-dual algorithms. Part I: Linear programming," Mathematical Programming 44 (1989) 27-42.
14. R.C. Monteiro, I. Adler and M.G.C. Resende, "A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension," Mathematics of Operations Research 15 (1990) 191-214.
15. S. Mizuno, M.J. Todd, and Y. Ye, "On adaptive-step primal-dual interior-point algorithms for linear programming," Mathematics of Operations Research 18 (1993) 964-981.
16. C. Roos and J.-Ph. Vial, "Long steps with the logarithmic penalty barrier function in linear programming," in: J. Gabszeywicz, J.F. Richard, and L. Wolsey, eds., Economic Decision Making: Games, Economics and Optimization (Elsevier Science Publishers, Amsterdam, 1989) pp. 433-441.
17. J. Renegar, "A polynomial-time algorithm based on Newton's method for linear programming," Mathematical Programming 40 (1988) 59-94.
18. G. Sonnevend, "An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming," in: Lecture Notes in Control and Information Sciences, Vol. 84 (Springer, New York, 1985) pp. 866-876.
19. R.J. Vanderbei, M.S. Meketon and B.A. Freedman, "A modification of Karmarkar's linear programming algorithm," Algorithmica 1 (1986) 395-407.
20. Y. Ye, M.J. Todd, and S. Mizuno, "An O(√n L)-iteration homogeneous and self-dual linear programming algorithm," Mathematics of Operations Research 19 (1994) 53-67.
21. L. Zhang and Y. Zhang, "On polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms," Technical Report 93-12, Department of Mathematics and Statistics, University of Maryland at Baltimore County, Baltimore, MD (1993).