Solving polynomial optimization problems via the truncated tangency variety and sums of squares

Journal of Pure and Applied Algebra

Volumn 213, Issue 11, 2009, Pages 2167-2176

  Hà, Huy Vui ^a   Pham, Tiên Son ^b  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

^b UNIVERSITY OF DALAT   (Viet Nam)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67349186860     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2009.03.014     Document Type: Article

References (24)

1. Benedetti R., and Risler J.-J. Real algebraic and semi-algebraic sets. Actualités Mathématiques (1990), Hermann
2. Demmel J., Nie J., and Powers V. Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals. J. Pure Appl. Algebra 209 1 (2007) 189-200
3. Garey M.R., and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness (1979), W.H. Freeman and Company
4. Hà H.V., and Pha{combining dot below}m T.S. Global optimization of polynomials using the truncated tangency variety and sums of squares. SIAM J. Optim. 19 2 (2008) 941-951
5. H.V. Hà, T.S. Pha{combining dot below}m, Optimization of polynomials on algebraic sets (submitted for publication)
6. Jelonek Z. Geometry of real polynomial mappings. Math. Z. 239 (2002) 321-333
7. Lasserre J.B. Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11 3 (2001) 796-817
8. Laurent M. Semidefinite representations for finite varieties. Math. Program. 109 1(A) (2007) 1-26
9. Loi T.L., and Zaharia A. Bifurcation sets of functions definable in o-minimal structures. Ill. J. Math. 42 3 (1998) 449-457
10. Marshall M. Optimization of polynomial functions. Canad. Math. Bull. 46 4 (2003) 575-587
11. Milnor J. Singular points of complex hypersurfaces. Annals of Mathematics Studies vol. 61 (1968), Princeton University Press
12. Némethi A., and Zaharia A. Milnor fibration at infinity. Indag. Math. 3 3 (1992) 323-335
13. Nesterov Y. Squared functional systems and optimization problems. In: Frenk H. (Ed). High Performance Optimization (2000), Kluwer Academic Publishers 405-440
14. Nie J., Demmel J., and Sturmfels B. Minimizing polynomials via sum of squares over the gradient ideal. Math. Prog. Ser. A 106 3 (2006) 587-606
15. Nocedal J., and Wright S.J. Numerical Optimization. Springer Series in Operations Research (1999), Springer-Verlag, New York
16. P.A. Parrilo, Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization, Ph.D. Thesis, California Institute of Technology, May 2000
17. Parrilo P.A., and Sturmfels B. Minimizing Polynomial Functions. DIMACS Series in Discrete Mathematics and Theoretical Computer Science vol. 60 (2003), AMS 83-99
18. Prajna S., Papachristodoulou A., and Parrilo P. SOSTOOLS User's Guide. http://control.ee.ethz.ch/~parrilo/SOSTOOLS/
19. Putinar M. Positive polynomials on compact semi-algebraic sets. Indiara Univ. Math. J. 42 3 (1993) 969-984
20. Schmüdgen K. The K-moment problem for compact semi-algebraic sets. Math. Ann. 289 2 (1991) 203-206
21. Schweighofer M. Global optimization of polynomials using gradient tentacles and sums of squares. SIAM J. Optim. 17 3 (2006) 920-942
22. Schweighofer M. Optimization of polynomials on compact semialgebraic sets. SIAM J. Optim. 15 3 (2005) 805-825
23. Shor N.Z. An approach to obtaining global extremums in polynomial mathematical programming problems. Kibernetika 5 (1987) 102-106
24. Yomdin Y., and Comte G. Tame Geometry with Application in Smooth Analysis (2004), Springer-Verlag, Berlin, Heidelberg