Ill-posedness and the complexity of deciding existence of solutions to linear programs

SIAM Journal on Optimization

Volumn 6, Issue 3, 1996, Pages 549-569

  Vera, Jorge R ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

Complexity of linear programming; Conditioning; Theory of linear programming

Indexed keywords

EID: 0030303849     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S105262349223352X     Document Type: Article

References (12)

1. L. BLUM, M. SHUB, AND S. SMALE, On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bull. Amer. Math. Soc., 21 (1989), pp. 1-46.
2. J. W. DEMMEL, On condition numbers and the distance to the nearest ill-posed problem, Numer. Math., 51 (1987), pp. 251-289.
3. _, The probability that a numerical analysis problem is difficult, Math. Comp., 50 (1988), pp. 449-480.
4. S. FILIPOWSKI, Towards a Computational Complexity Theory that Uses Approximate Data and Knowledge, Ph.D. dissertation, Cornell University, Ithaca, NY, 1993.
5. G. H. GOLUB AND C. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
6. J. RENEGAR, A polynomial-time algorithm based on Newton's method for linear programming, Math. Programming, 40 (1988), pp. 59-94.
7. _, Is It Possible to Know a Problem Instance Is Ill-Posed? Some Foundations for a General Theory of Condition Number, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, Tech. report 939, October 1990.
8. _, Incorporating condition measures into the complexity theory of linear programming, SIAM J. Optim., 5 (1995), pp. 506-524.
9. _, Linear programming, complexity theory and elementary functional analysis, Math. Programming, 70 (1995), pp. 279-351.
10. S. SMALE, Some remarks on the foundations of numerical analysis, SIAM Rev., 32 (1990) pp. 211-220.
11. P. VAIDYA, A locally well-behaved potential function and a simple Newton-type method for finding the center of a polytope, in Progress in Mathematical Programming-Interior Point and Related Methods, N. Megiddo, ed., Springer-Verlag, Berlin, 1989, pp. 79-90.
12. J. VERA, Ill-Posedness in Mathematical Programming and Problem Solving with Approximate Data, Ph.D. dissertation, Cornell University, Ithaca, NY, 1992.