Theoretical rate of convergence for interval inclusion functions

Journal of Global Optimization

Volumn 53, Issue 4, 2012, Pages 749-767

  Scholz, Daniel ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Approximation algorithms; Continuous problems; Facility location problems; Geometric branch and bound; Global optimization; Interval analysis

Indexed keywords

BENCH-MARK PROBLEMS; BOUND METHOD; BRANCH AND BOUNDS; CENTERED FORM; CONTINUOUS PROBLEMS; FACILITY LOCATION PROBLEM; INCLUSION FUNCTION; INTERVAL ANALYSIS; INTERVAL BRANCH-AND-BOUND METHOD; INTERVAL EXTENSION; LOWER BOUNDS; NON-CONVEX GLOBAL OPTIMIZATION; NUMERICAL STUDIES; RATE OF CONVERGENCE; SOLUTION ALGORITHMS; THEORETICAL POINTS; THEORETICAL RATES; WEBER PROBLEM;

APPROXIMATION ALGORITHMS; APPROXIMATION THEORY; BRANCH AND BOUND METHOD; GEOMETRY;

GLOBAL OPTIMIZATION;

EID: 84863724010     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-011-9735-9     Document Type: Article

References (21)

1. Baumann, E.: Optimal centered forms. BIT Numer. Math. 28, 80-87 (1988)
2. Blanquero, R., Carrizosa, E.: Continuous location problems and big triangle small triangle: constructing better bounds. J. Global Optim. 45, 389-402 (2009)
3. Chuba, W., Miller, W.: Quadratic convergence in interval arithmetic. Part I. BIT Numer. Math. 12, 284-290 (1972)
4. Csallner, A. E., Csendes, T.: The convergence speed of interval methods for global optimization. Comput. Math. Appl. 31, 173-178 (1996)
5. Drezner, Z., Suzuki, A.: The big triangle small triangle method for the solution of nonconvex facility location problems. Oper. Res. 52, 128-135 (2004)
6. Fernández, J., Pelegrín, B., Plastria, F., Tóth, B.: Solving a Huff-like competitive location and design model for profit maximization in the plane. Eur. J. Oper. Res. 179, 1274-1287 (2007)
7. Floudas, C. A., Pardalos, P. M.: Encyclopedia of Optimization. 2nd edn. Springer, New York (2009)
8. Hansen, E.: Global Optimization Using Interval Analysis. 1st edn. Marcel Dekker, New York (1992)
9. Hansen, P., Peeters, D., Richard, D., Thisse, J. F.: Theminisum andminimax location problems revisited. Oper. Res. 33, 1251-1265 (1985)
10. Horst, R., Pardalos, P. M., Thoai, N. V.: Introduction to Global Optimization. 2nd edn. Springer, Berlin (2000)
11. Krawczyk, R., Nickel, K.: Die zentrische Form in der Intervallarithmetik, ihre quadratische Konvergenz und ihre Inklusionsisotonie. Computing 28, 117-137 (1982)
12. Neumaier, A.: Interval Methods for Systems of Equations. 1st edn. Cambridge University Press, Cambridge (1990)
13. Plastria, F.: GBSSS: the generalized big square small square method for planar single-facility location. Eur. J. Oper. Res. 62, 163-174 (1992)
14. Ratschek, H., Rokne, J.: NewComputer Methods forGlobalOptimization. 1st edn. Ellis Horwood, Chichester, England (1988)
15. Ratschek, H., Voller, R. L.: What can interval analysis do for global optimization?. J. Global Optim. 1, 111-130 (1991)
16. Schöbel, A., Scholz, D.: The theoretical and empirical rate of convergence for geometric branch-and-bound methods. J. Global Optim. 48, 473-495 (2010)
17. Schwefel, H. P.: Numerical Optimization of Computer Models. 1st edn. Wiley, New York (1981)
18. Tóth, B., Csendes, T.: Empirical investigation of the convergence speed of inclusion functions in a global optimization context. Reliab. Comput. 11, 253-273 (2005)
19. Tóth, B., Fernández, J., Csendes, T.: Empirical convergence speed of inclusion functions for facility location problems. J. Comput. Appl. Math. 199, 384-389 (2007)
20. Tóth, B., Fernández, J., Pelegrín, B., Plastria, F.: Sequential versus simultaneous approach in the location and design of two new facilities using planar Huff-like models. Comput. Oper. Res. 36, 1393-1405 (2009)
21. Tuy, H., Al-Khayyal, F., Zhou, F.: A D. C. optimization method for single facility location problems. J. Global Optim. 7, 209-227 (1995)