Sharp upper bound for the expected number of shadow vertices in LP-polyhedra under orthogonal projection on two-dimensional planes

Mathematics of Operations Research

Volumn 24, Issue 3, 1999, Pages 544-603

  Borgwardt, Karl Heinz ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; LINEAR PROGRAMMING; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING; VECTORS;

ORTHOGONAL PROJECTIONS; ROTATION SYMMETRY MODELS (RSM); SHADOW VERTIX ALGORITHMS;

OPERATIONS RESEARCH;

EID: 0033358820     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.24.3.544     Document Type: Article

References (17)

1. 2)) expected number of steps. J. Complexity 3 372-387.
2. _, N. Megiddo. 1985. A simplex algorithm where the average number of steps is bounded between two quadratic functions of the smaller dimension. J. ACM 32 871-895.
3. Borgwardt, K. H. 1977. Untersuchungen zur asymptotik der mittleren schrittzahl von simplexverfahren in der linearen optimierung. Dissertation, Universität Kaiserslautern.
4. _ 1982a. Some distribution-independent results about the asymptotic order of the average number of pivot steps of the simplex method. Math. Oper. Res. 7 441-462.
5. _ 1982b. The average number of pivot steps required by the simplex-method is polynomial. Zeitschrift für Oper. Res. 26 157-177.
6. _ 1987. The Simplex Method, A Probabilistic Analysis. Springer Verlag, Heidelberg.
7. _, R. Damm, R. Donig, G. Joas. 1993. Empirical studies on the average efficiency of simplex variants under rotation symmetry. ORSA J. Comput. 5 249-260.
8. _ 1994a. Verschärfung des polynomialitätsbeweises für die erwartete anzahl von schattenecken im rotations-symmetrie-modell. In E. Schock, ed., Beiträge zur Angewandten Analysis und Informatik, Festschrift zu Ehren von Helmut Brakhage, Shaker Verlag, Aachen.
9. _ 1994b. Improving the theoretical upper bound for the expected number of shadow-vertices in the Rotation-Symmetry-Model. Schwerpunktreport der Deutschen Forschungsgemeinschaft Nr. 537, Universität Augsburg.
10. Haimovich, M. 1983. The simplex algorithm is Very Good! - On the expected number of pivot steps and related properties of random linear programs. Report, Columbia University, New York.
11. Höfner, G. 1995. Lineare optimierung mit dem schatteneckenalgorithmus - Untersuchungen zum mittleren rechenaufwand und entartungsverhalten. Dissertation, Universität Augsburg.
12. Huhn, P. 1997. Schranken für die durchschnittliche laufzeit von simplexverfahren und innere-punkl-verfahren. Dissertation, Universität Augsburg.
13. Küfer, K. 1995. On the variance of the number of pivot steps required by the simplex algorithm. Math. Methods Oper. Res. 42 1-24.
14. _ 1996. An improved asymptotic analysis of the number of pivot steps required by the simplex algorithm. Math. Methods of Oper. Res. 44 147-170.
15. Shamir, R. 1987. The efficiency of the simplex method. Management Sci. 33 301-334.
16. Smale, S. 1983. On the average speed of the simplex method of linear programming. Math. Programming 27 241-262.
17. Todd, M. J. 1986. Polynomial expected behavior of a pivoting algorithm for linear complimentarity and linear programming problems. Math. Programming 35 173-192.