On the complexity of Schmüdgen's Positivstellensatz

Journal of Complexity

Volumn 20, Issue 4, 2004, Pages 529-543

  Schweighofer, Markus ^a  

^a UNIVERSITY OF KONSTANZ   (Germany)

Author keywords

Complexity; Moment problem; Optimization of polynomials; Positive polynomial; Positivstellensatz; Preordering; Sum of squares

Indexed keywords

EID: 3242670924     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jco.2004.01.005     Document Type: Article

References (20)

1. Berr R. Wörmann T. Positive polynomials on compact sets Manuscripta Math. 104 2001 135-143
2. Bochnak J. Coste M. Roy M.-F. Real algebraic geometry Ergebnisse der Mathematik und ihrer Grenzgebiete Vol. 36 1998 Springer Berlin
3. Jacobi T. Prestel A. Distinguished representations of strictly positive polynomials J. Reine Angew. Math. 532 2001 223-235
4. Lasserre J.B. Global optimization with polynomials and the problem of moments SIAM J. Optim. 11 3 2001 796-817
5. de Loera J.A. Santos F. An effective version of Pólya's theorem on positive definite forms J. Pure Appl. Algebra 108 3 1996 231-240 erratum J. Pure Appl. Algebra 155 (2001) 309-310
6. Marshall M. Optimization of polynomial functions Canad. Math. Bull. 46 2003 575-587
7. Mauch E. Complexity estimates for representations of Schmüdgen type J. Complexity 18 1 2002 346-355
8. P. Parrilo, B. Sturmfels, Minimizing polynomial functions, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 60, American Mathematical Society, Providence, RI, 2003, pp. 83-100
9. Pólya G. Über positive Darstellung von Polynomen Vierteljahresschrift der Naturforschenden Gesellschaft in Zürich 73 1928 141-145 reprinted in: Collected Papers, Vol. 2, MIT Press, Cambridge, 1974, pp. 309-313
10. Powers V. Reznick B. A new bound for Pólya's theorem with applications to polynomials positive on polyhedra J. Pure Appl. Algebra 164 1-2 2001 221-229
11. Prestel A. Delzell C. Positive Polynomials, Springer Monographs in Mathematics 2001 Springer Berlin
12. Putinar M. Positive polynomials on compact semi-algebraic sets Indiana Univ. Math. J. 42 3 1993 969-984
13. Reznick B. Uniform denominators in Hilbert's seventeenth problem Math. Z. 220 1 1995 75-97
14. J. Schmid, On the degree complexity of Hilbert's 17th problem and the Real Nullstellensatz, Habilitationsschrift, Universität Dortmund, 1998
15. Schmüdgen K. The K-moment problem for compact semi-algebraic sets Math. Ann. 289 2 1991 203-206
16. Schweighofer M. An algorithmic approach to Schmüdgen's Positivstellensatz J. Pure Appl. Algebra 166 3 2002 307-319
17. M. Schweighofer, Optimization of polynomials on compact semialgebraic sets, submitted, http://www.mathe.uni-konstanz.de/homepages/schweigh/
18. Solernó P. Effective Łojasiewicz inequalities in semialgebraic geometry Appl. Algebra Eng. Comm. Comput. 2 1 1991 1-14
19. Stengle G. Complexity estimates for the Schmüdgen Positivstellensatz J. Complexity 12 2 1996 167-174
20. Sturmfels B. Solving systems of polynomial equations CBMS Regional Conference Series in Mathematics Vol. 97 2002 American Mathematical Society Providence, RI