Simulation and optimization by quantifier elimination

Journal of Symbolic Computation

Volumn 24, Issue 2, 1997, Pages 189-208

  Weispfenning, Volker ^a  

^a UNIVERSITY OF PASSAU   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031208898     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1997.0122     Document Type: Article

References (34)

1. Bareiss, E.H. (1968). Sylvester's identity and multistep integer preserving Gaussian elimination, Math. Comput. 22, 565-578.
2. Burhenne, K.-D. (1990). Quantorenelimination für lineare Probleme mit Gleichungen und Ungleichungen, Diplomarbeit, Universität Passau.
3. Černikov, R.N. (1961). The solution of linear programming problems by elimination of unknowns. Dokl. Akad. Nauk 139, 1314-1317. [Translation in: (1961) Soviet Math. Dokl. 2, 1099-1103.]
4. Černikov, R.N. (1961). The solution of linear programming problems by elimination of unknowns. Dokl. Akad. Nauk 139, 1314-1317. [Translation in: (1961) Soviet Math. Dokl. 2, 1099-1103.]
5. Chandru, V. (1993). Variable elimination in linear constraints, Computer J. 36, 463-472.
6. Chvátal, V. (1983). Linear Programming, A Series of Books in the Mathematical Sciences, V. Klee, (ed.), New York/San Francisco, W.H. Freeman and Company.
7. Collins, G.E., Hong, H. (1991). Partial cylindrical algebraic decomposition for quantifier elimination. J. Symbolic Comput. 12, 299-328.
8. Dantzig, G.B. (1966). Lineare Programmierung und Erweiterungen, Springer-Verlag.
9. Dines, L.L. (1919). Systems of linear inequalities, Ann. Math. 20, 191-199.
10. Dolzmann, A., Sturm, T. (1995). Simplification of quantifier-free formulas over ordered fields. Preprint MIP-9517, Universität Passau, J. Symbolic Comput., 24:209-231.
11. Dolzmann, A., Sturm, T. (1996). REDLOG, Computer algebra meets computer logic. Preprint MIP-9603, Universität Passau.
12. Dolzmann, A., et al. (1996). A new approach for automatic theorem proving in real geometry. Preprint MIP 9611, Universität Passau, J. Autom. Reasoning, (in press).
13. Dorato, P., Yang, W., Abdallah, C.T. (1995). Application of quantifier elimination to robust multi-objective feedback design, talk at the IMACS conference on applications of computer algebra, Albuquerque, NM, May 1995.
14. Eaves, B.C., Rothblum, U.G. (1989). A theory on extending algorithms for parametric problems. Math. Oper. Res. 14, 502-533.
15. Eaves, B.C., Rothblum, U.G. (1992). Dines-Fourier-Motzkin quantifier elimination and an application of corresponding transfer principles over ordered fields, Math. Programming 53, 307-321.
16. Eaves, B.C., Rothblum, U.G. (1994). Formulation of linear problems and solution by a universal machine, Math. Programming 65, 263-310.
17. Fourier, J.B.J. (1826). Solution d'une question particulière du calcul des inégalités (1826) and excerpts from Histoire de l'Académie, 1823, 1824, Oeuvres II, 317-328.
18. Imbert, J.-L. (1993). Variable elimination for disequations in generalized linear constraint systems. Computer J. 36, 473-484.
19. Jeroslow, R.G. (1973a). Asymptotic linear programming. Oper. Res. 21, 1128-1141.
20. Jeroslow, R.G. (1973b). Linear programs dependent on a single parameter. Discrete Math. 6, 119-140.
21. Kappert, M. (1995). Eliminationsverfahren zur linearen und quadratischen Optimierung. Diplomarbeit, Universität Passau.
22. Liska, R. Steinberg, S. (1993). Applying quantifier elimination stability analysis of differential schemes. Computer J. 36, 497-503.
23. Liska, R., Steinberg, S. (1994). Using computer algebra to test stability, working notes, Oct. 1994.
24. Loos, R., Weispfenning, V. (1993). Applying linear quantifier elimination. Computer J. 36, 450-462.
25. Motzkin, T.S. (1936). Beiträge zur Theorie der linearen Ungleichungen. Dissertation, Universität Zürich.
26. Neun, W., Sturm, T. (1995). Parallelizing an elimination method for linear programming, work in progress at the ZIB, Berlin, since June 1995.
27. Renegar, J. (1992). On the computational complexity and geometry of the first-order theory of the reals, parts I, II, III, J. Symbolic Comput. 13, 155-352.
28. Schrijver, A. (1986). Theory of Linear and Integer Programming. Chichester, Wiley.
29. Sturm, T. (1993). REDUCE-implementation of the algorithms in Loos, R., Weispfenning, V. (1993), Passau.
30. Weispfenning, V. (1988). The complexity of linear problems in fields. J. Symbolic Comput. 5, 3-27.
31. Weispfenning, V. (1994). Quantifier elimination for real algebra - the cubic case. In J. von zur Gathen, M. Giesbrecht (eds), Proceedings ISSAC 94, pp. 258-263. New York, ACM Press.
32. Weispfenning, V. (1997a). Parametric linear, quadratic and hyperbolic optimization by elimination. J. Symbolic Comput. To appear.
33. Weispfenning, V. (1997b). Quantifier Elimination for real Algebra - the Quadratic Case and beyond. J. AAECC. 8, 85-101.
34. Williams, H.P. (1986). Fourier's method of linear programming and its dual. Amer. Math. Monthly 93, 681-695.