Linear programming in O(n3/ln n L) Operations

SIAM Journal on Optimization

Volumn 9, Issue 4, 1999, Pages 803-812

  Anstreicher, K M ^a,b  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Conjugate gradient method; Interior point algorithm; Linear programming; Partial updating

Indexed keywords

EID: 0033436756     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623497323194     Document Type: Article

References (15)

1. K. M. ANSTREICHER, A standard form variant, and safeguarded linesearch, for the modified Karmarkar algorithm, Math. Programming, 47 (1990), pp. 337-351.
2. D. COPPERSMITH AND S. WINOGRAD, Matrix multiplication via arithmetic progressions, in Proceedings of the 19th Annual ACM Symposium on Theory of Computing, 1986, pp. 1-6.
3. P. E. GILL, W. MURRAY, AND M. H. WRIGHT, Practical Optimization, Academic Press, New York, 1981.
4. 3L) operations, in Progress in Mathematical Programming, N. Megiddo, ed., Springer-Verlag, New York, 1987.
5. N. KARMARKAR, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), pp. 373-395.
6. D. G. LUENBERGER, Linear and Nonlinear Programming, 2nd ed., Addison-Wesley, New York, 1984.
7. R. D. C. MONTEIRO AND I. ADLER, Interior path following primal-dual algorithms. Part I: Linear programming, Math. Programming, 44 (1989), pp. 27-41.
8. Y. NESTEROV, Introductory Lectures on Convex Programming, Vol. I: Basic Course, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, 1996.
9. Y. NESTEROV AND A. NEMIROVSKII, Acceleration and parallelization of the path-following interior point method for a linearly constrained quadratic programming problem, SIAM J. Optim., 1 (1991), pp. 548-564.
10. Y. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia, 1994.
11. J. RENEGAR, A polynomial-time algorithm, based on Newton's method, for linear programming, Math. Programming, 40 (1988), pp. 59-93.
12. C. ROOS AND J.-PH. VIAL, A polynomial method of approximate centers for linear programming, Math. Programming, 54 (1992), pp. 295-305.
13. D. F. SHANNO, Computing Karmarkar projections quickly, Math. Programming, 41 (1988), pp. 61-71.
14. P. M. VAIDYA, Speeding-up linear programming using fast matrix multiplication, in Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, 1989, pp. 338-343.
15. 1.5n)L) arithmetic operations, Math. Programming, 47 (1990), pp. 175-201.