Safety verification of iterative algorithms over polynomial vector fields

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 6061-6067

  Roozbehani, Mardavij ^a   Megretski, Alexandre ^b   Feron, Eric ^c  

^a Massachusetts Institute of Technology   (United States)

^b MIT MEDIA LAB   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION MAKING; NEWTON-RAPHSON METHOD; ONLINE SYSTEMS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

ITERATIVE ALGORITHMS; ONLINE OPTIMIZATION; POLYNOMIAL VECTOR FIELDS; SAFETY VERIFICATION;

ALGORITHMS;

EID: 39649090080     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377333     Document Type: Conference Paper

References (10)

1. J. Bochnak, M. Coste, and M. F. Roy- Real Algebraic Geometry, Springer 1998.
2. J. Hubbard, D. Schleicher and S. Sutherland, How to find all roots of complex polynomials by Newton's method, Inventiones Mathematcae. 146 (2001), 1-33.
3. A. Megretski. Positivity of trigonometric polynomials. In Proc. 42nd, IEEE Conference on Decision and Conlrol, Hawaii, December 9-12, 2003.
4. P. A. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, California Institute of Technology, (Ph.D. Thesis), Pasadena, CA, May 2000.
5. P. A. Parrilo. Minimizing Polynomial Functions. In Algorithmic and Quantitative Reftl Algebraic Geometry, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. Vol. 60. pp. 83-99, AMS.
6. K. Gatermann, and P.A. Pernio. Symmetry groups, semidefinite programs, and sums of squares. Journal of Pure: and Appl. Algebra, Vol. 192, No. 1-3, pp. 95-128, 2004.
7. http://pinopt.com
8. S. Prajna, A. Fapachristodoulou, P. Seiler, and P. A. Parrilo, SOSTOOLS: Sum, of squares optimization toolbox for MATLAB, 2004. http://www.mit.edu/ parrilosostools,
9. th International Workshop, Zurich, Switzerland. Lecture Notes in Computer Science 3414, Springer 2005, pp. 606-622.
10. M. Roozbehani, A. Megretski, E, Feron, Convex optimization proves, software correctness. In Proceedings of the 2005 American Control Conference, Portland, Oregon, June 2005.