On the complexity of computing estimates of condition measures of a conic linear system

Mathematics of Operations Research

Volumn 28, Issue 4, 2003, Pages 625-648

  Freund, Robert M ^a   Vera, Jorge R ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

Author keywords

Complexity of linear programming; Complexity theory; Conditioning; Error analysis; Interior point methods; Semidefinite programming

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; ESTIMATION; VECTORS;

COMPLEXITY THEORY; CONDITIONING; INTERIOR POINT METHODS; SEMIDEFINITE PROGRAMMING;

LINEAR PROGRAMMING;

EID: 3142694756     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.28.4.625.20509     Document Type: Article

References (19)

1. Epelman, M., R. M. Freund. 2000. Condition number complexity of an elementary algorithm for computing a reliable solution of a conic linear system. Math. Programming 88(3) 451-485.
2. Filipowski, S. 1997. On the complexity of solving sparse symmetric linear programs specified with approximate data. Math. Oper. Res. 22 769-792.
3. Filipowski, S. 1999. On the complexity of solving linear programs specified with approximate data and known to be feasible. SIAM J. Optim. 9 1010-1040.
4. Freund, R. M., J. B. Orlin. 1985. On the complexity of four polyhedral set containment problems. Math. Programming 33 133-145.
5. Freund, R. M., J. R. Vera. 2000a. Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm. SIAM J. Optim. 10(1) 155-176.
6. Freund, R. M., J. R. Vera. 2000b. Some characterizations and properties of the "distance to ill-posedness" and the condition measure of a conic linear system. Math. Programming 86 225-260.
7. Grötschel, M., L. Lovasz, A. Schrijver. 1988. Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin, Germany.
8. Mangasarian, O. 1987. Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems. SIAM J. Control Optim. 25(3) 41-87.
9. Nesterov, Y., A. Nemirovskii. 1994. Interior-Point Polynomial Algorithms in Convex Programming. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
10. Nunez, M. A., R. M. Freund. 1998. Condition measures and properties of the central trajectory of a linear program. Math. Programming 83(1) 1-28.
11. Pena, J. 1997. Computing the distance to infeasibility: Theoretical and practical issues. Technical report, Cornell University, Center for Applied Mathematics, Ithaca, NY.
12. Renegar, J. 1994. Some perturbation theory for linear programming. Math. Programming 65(1) 73-91.
13. Renegar, J. 1995a. Incorporating condition measures into the complexity theory of linear programming. SIAM J. Optim. 5(3) 506-524.
14. Renegar, J. 1995b. Linear programming, complexity theory, and elementary functional analysis. Math. Programming 70(3) 279-351.
15. Renegar, J. 1996. Condition numbers, the barrier method, and the conjugate gradient method. SIAM J. Optim. 64(4) 879-912.
16. Vera, J. R. 1992. Ill-posedness in mathematical programming and problem solving with approximate data. Ph.D. thesis, Cornell University, Ithaca, NY.
17. Vera, J. R. 1996. Ill-posedness and the complexity of deciding existence of solutions to linear programs with approximate data. SIAM J. Optim. 6(3) 549-569.
18. Vera, J. R. 1998. On the complexity of linear programming under finite precision arithmetic. Math. Programming 80(1) 91-123.
19. Yudin, D. B., A. S. Nemirovskii. 1976. Informational complexity and efficient methods for solving complex extremal problems. Ekonomika i Matem. Metody 12 357-369.