Verified global optimization with Taylor model based range bounders

WSEAS Transactions on Computers

Volumn 4, Issue 11, 2005, Pages 1611-1618

  Makino, Kyoko ^a   Berz, Martin ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

COSY GO; Global optimization; Linear dominated bounder LDB; Quadratic fast bounder QFB; Taylor model; Verified computations

Indexed keywords

COMPUTATIONAL METHODS; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIALS;

LINEAR DOMINATED BOUNDER (LDB); QUADRATIC FAST BOUNDER (QFB); RANGE BOUNDERS; TAYLOR MODEL; VERIFIED COMPUTATIONS; VERIFIED GLOBAL OPTIMIZATION;

COMPUTER SIMULATION;

EID: 33645115495     PISSN: 11092750     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. K. Makino and M. Berz. Taylor models and other validated functional inclusion methods. International Journal of Pure and Applied Mathematics, 6,3:239-316, 2003. http://bt.pa.msu.edu/pub.
2. K. Makino. Rigorous Analysis of Nonlinear Motion in Particle Accelerators. PhD thesis, Michigan State University, East Lansing, Michigan, USA, 1998. Also MSUCL-1093.
3. M. Berz, J. Hoefkens, and K. Makino. COSY INFINITY Version 8.1 - programming manual. Technical Report MSUHEP-20703, Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, 2002.
4. See also http://cosy.pa.msu.edu.
5. N. Revol, K. Makino, and M. Berz. Taylor models and floating-point arithmetic: Proof that arithmetic operations are validated in COSY. Journal of Logic and Algebraic Programming, in print, 2004. University of Lyon LIP Report RR 2003-11, MSU Department of Physics Report MSUHEP-30212, http://bt.pa.msu.edu/pub.
6. M. Berz and K. Makino. Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliable Computing, 4(4):361-369, 1998.
7. K. Makino and M. Berz. Suppression of the Wrapping Effect by Taylor Model based Validated Integrators. Submitted. Also MSUHEP-040910, available at http://bt.pa.msu.edu/pub.
8. M. Berz and J. Hoefkens. Verified high-order inversion of functional dependencies and superconvergent interval Newton methods. Reliable Computing, 7(5):379-398, 2001.
9. K. Makino and M. Berz. COSY INFINITY version 9. Nuclear Instruments and Methods, in print.
10. R. E. Moore. Private communication.
11. More, Garbow, and Hillstrom. Testing unconstrained optimization software. ACM Trans. Math. Software, 7:17-41, 1981.
12. R. B. Kearfott. Rigorous Global Search: Continuous Problems. Kluwer, 1996.