Computing slope enclosures by exploiting a unique point of inflection

Applied Mathematics and Computation

Volumn 204, Issue 1, 2008, Pages 249-256

  Schnurr, Marco ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Automatic slope computation; Interval analysis; Interval slope; Slope enclosure

Indexed keywords

GLOBAL OPTIMIZATION; MATHEMATICAL PROGRAMMING;

AUTOMATIC SLOPE COMPUTATION; CONCAVE FUNCTIONS; INTERVAL ANALYSIS; INTERVAL SLOPE; POINT OF INFLECTION; SLOPE ENCLOSURE;

ENCLOSURES;

EID: 52049106386     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.06.041     Document Type: Article

References (18)

1. M. Schnurr, Steigungen höherer Ordnung zur verifizierten globalen Optimierung, Ph.D. Thesis, Universität Karlsruhe, 2007. .
2. Moore R.E. Interval Analysis (1966), Prentice Hall, Englewood Cliffs, NJ
3. Alefeld G., and Herzberger J. Introduction to Interval Computations (1983), Academic Press, New York
4. Frommer A., Lang B., and Schnurr M. A comparison of the Moore and Miranda existence tests. Computing 72 (2004) 349-354
5. Goldsztejn A. Comparison of the Hansen-Sengupta and the Frommer-Lang-Schnurr existence tests. Computing 79 (2007) 53-60
6. Moore R.E. A test for existence of solutions to nonlinear systems. SIAM J. Numer. Anal. 14 4 (1977) 611-615
7. Schäfer U., and Schnurr M. A comparison of simple tests for accuracy of approximate solutions to nonlinear systems with uncertain data. J. Ind. Manag. Optim. 2 4 (2006) 425-434
8. Schnurr M. On the proofs of some statements concerning the theorems of Kantorovich, Moore, and Miranda. Reliab. Comput. 11 (2005) 77-85
9. Hansen E.R., and Walster G.W. Global Optimization Using Interval Analysis. second ed. (2004), Marcel Dekker, New York Revised and expanded
10. Kearfott R.B. Rigorous Global Search: Continuous Problems (1996), Kluwer Academic Publishers, Dordrecht
11. Ratz D. Automatic Slope Computation and its Application in Nonsmooth Global Optimization (1998), Shaker Verlag, Aachen
12. Ratz D. A nonsmooth global optimization technique using slopes - the one-dimensional case. J. Global Optim. 14 (1999) 365-393
13. M. Schnurr, A second-order pruning step for verified global optimization, Journal of Global Optimization, in press.
14. Rall L.B. Automatic Differentiation Techniques and Applications. Lecture Notes in Computer Science vol. 120 (1981), Springer, Berlin
15. Krawczyk R., and Neumaier A. Interval slopes for rational functions and associated centered forms. SIAM J. Numer. Anal. 22 (1985) 604-616
16. Shen Z., and Wolfe M.A. On interval enclosures using slope arithmetic. Appl. Math. Comput. 39 (1990) 89-105
17. Kolev L. Use of interval slopes for the irrational part of factorable functions. Reliab. Comput. 3 (1997) 83-93
18. Deuflhard P., and Hohmann A. Numerical Analysis (1995), de Gruyter, Berlin