An O(√n L) iteration bound primal-dual cone affine scaling algorithm for linear programming

Mathematical Programming, Series B

Volumn 72, Issue 2, 1996, Pages 177-194

  Sturm, Jos F ^a   Zhang, Shuzhong ^b  

^a TINBERGEN INSTITUTE   (Netherlands)

^b ERASMUS UNIVERSITY ROTTERDAM   (Netherlands)

Author keywords

Affine scaling; Linear programming; Polynomiality; Primal dual interior point algorithm

Indexed keywords

EID: 0039924574     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. I. Adler, M.G.C. Resende, G. Veiga and N.K. Karmarkar, "An implementation of Karmarkar's algorithm for linear programming," Mathematical Programming 44 (1989) 297-335.
2. D. Den Hertog and C. Roos, "A survey of search directions in interior point methods for linear programming," Mathematical Programming 52 (1991) 481-509.
3. I.I. Dikin, "Iterative solution of problems of linear and quadratic programming," Soviet Mathematics Doklady 8 (1967) 674-675.
4. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques (Wiley, New York, 1968).
5. D. Goldfarb and D. Xiao, "A primal projective interior point method for linear programming," Mathematical Programming 51 (1991) 17-43.
6. C.C. Gonzaga, "Conical projection algorithms for linear programming," Mathematical Programming 43 (1989) 151-173.
7. C.C. Gonzaga, "Search directions for interior linear programming methods," Algorithmica 6 (1991) 153-181.
8. C.C. Gonzaga, "The largest step path following algorithm for monotone linear complementarity problems," Report 94-07, Delft University of Technology, (1994).
9. J.N. Hooker, "Karmarkar's linear programming algorithm," interfaces 16 (1986) 75-90.
10. P. Huard, "Resolution of mathematical programming with nonlinear constraints by the method of centres," in: J. Abadie, ed., Nonlinear Programming (North Holland, Amsterdam, 1967) pp. 207-219.
11. G-M. Jan and S-C Fang, "A new variant of the primal affine scaling algorithm for linear programs", Optimization 22 (1991) 681-715.
12. B. Jansen, C. Roos and T. Terlaky, "A polynomial primal-dual Dikin-type algorithm for linear programming," Report 93-36, Delft University of Technology, (1993).
13. B. Jansen, C. Roos, T. Terlaky and J.-Ph. Vial, "Interior-point methodology for linear programming: Duality, sensitivity analysis and computational aspects," Report 93-28, Delft University of Technology, (1993).
14. N.K. Karmarkar, "A new polynomial-time algorithm for linear programming," Combinatorica 4 (1984) 373-395.
15. M. Kojima, N. Megiddo, T. Noma and A. Yoshise, A unified approach to interior point algorithms for linear complementarity problems, Lecture Notes in Computer Science, Vol. 538 (Springer, Berlin, 1991).
16. 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. 29-48.
17. N. Megiddo, "On the complexity of linear programming," in: T. Bewley, ed., Advances in Economic Theory (Cambridge University Press, Cambridge, 1987) pp. 225-268.
18. S. Mizuno and A. Nagasawa, "A primal-dual affine scaling potential reduction algorithm for linear programming," Mathematical Programming 62 (1993) 119-131.
19. S. Mizuno, M.J. Todd and Y. Ye, "On adaptive-step primal-dual interior-point algorithms for linear programming," Mathematics of Operations Research (1993) 964-981.
20. R.D.C. Monteiro and I. Adler, "Interior path following primal-dual algorithm," Mathematical Programming 44 (1989) 27-42.
21. R.D.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.
22. M.W. Padberg, "Solution of a nonlinear programming problem arising in the projective method for linear programming," Manuscript, School of Business and Administration, New York University (New York, 1985).
23. C.H. Papadimitriou and K. Steiglitz, Combinatorial Optimization, Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, NJ, 1982).
24. J. Renegar, "A polynomial-time algorithm, based on Newton's method, for linear programming," Mathematical Programming 40 (1988) 59-93.
25. J.F. Sturm and S. Zhang, "New complexity results for the Iri-Imai method," Research Memorandum 530, University of Groningen (Groningen, 1993). To appear in Annals of Operations Research.
26. T. Tsuchiya, "Global convergence of the affine scaling methods for degenerate linear programming problems," Mathematical Programming 52 (1991) 377-404.
27. T. Tsuchiya and M. Muramutsu, "Global convergence of the long-step affine scaling algorithm for degenerate linear programming problems," SIAM Journal on Optimization 5 (1995) 525-551.
28. L. Tunçel, "Constant potential primal-dual algorithm: A framework," Mathematical Programming 66 (1994) 145-159.
29. H. Yamashita, A Polynomially and Quadratically Convergent Method for Linear Programming (Mathematical Systems Inc., Tokyo, 1986).
30. 3Z.) potential reduction algorithm for linear programming," Mathematical Programming 50 (1991) 239-258.