A global optimization using interval arithmetic

Ismail Mohd


In order to establish an algorithm for bounding the global minimizers of a twice continuously differentiable function f :Rn → R1 in a given box ( a compact interval in Rn ) using interval arithmetic, which is superior in the sense of less time needed compared to other method ([2]), in this paper we will attempt to describe as much as possible the ideas which presents and fulfill the explicitly mentioned algorithm.


Interval mathematics; Symmetric operator; Lagrange multiplier; Gauss algorithm;

Full Text:



Bailey, P. J., Cole, A. J., and Morrison, R., Triplex User Manual, University of St. Andrews Department

of Computational Science Report CS/82/5, 1982.

Hansen, E. R., Numerische Mathematik 34 (1980) 247 – 270.

Ichida, K., and Fujii, Y., Computing 23 (1979) 85 – 97.

Ismail, B. M., Applied Mathematics and Computation, 1989

Ismail, B. M., Pertanika 13(3) (1990) 409 -413.

Ismail, B. M., Computational and Applied Mathematics, 31(1990) 373 – 382.

Ismail, B. M., Asean Journal on Science and Technology for Development, 7(2)(1990) 1 – 11.

Ismail, B. M., Computational and Applied Mathematics, 58(1995) 183 – 192.

Ismail, B. M., Applied Mathematics and Computation, 110(2000) 121 - 131.

Jones, S. T., Searching for Solutions of Finite Nonlinear Systems – An Interval Approach, Ph. D. Thesis, University of Winsconsin, Madison U.S.A., 1978.

Morrison, R., Cole, A. J., Bailey, P. J., Wolfe, M. A., and Shearer, J. M., Experience in Using a High Level Language that Supports Interval Arithmetic, In proceedings of ARITH6, the Joint TCCA/IEEE Sixth Symposium on Computer Arithmetic, Aarhus, Denmark, 1983.

Moore, R. E., and Jones, S. T., SIAM Journal on Numerical Analysis, 14(1977) 1051 – 1065.

Nickel, K. L. E., On the Newton Method in Interval Analysis, MRC Technical Summary Report 1136 (1971) Madison, Wisconsin, U. S. A.

Robinson, S. M., Mathematical Programming, 5 (1973) 235 – 242.

Shearer, J. M., and Wolfe, M. A., SIAM Journal on Numerical Analysis 22(1985) 1200 – 1207.

Shearer, J. M., and Wolfe, M. A., Applied Mathematics and Computation 17(1985) 229 - 239.

Shearer, J. M., and Wolfe, M. A., SIAM Journal on Scientific and Statistical Computing, 1986.

DOI: https://doi.org/10.11113/mjfas.v2n1-2.17


  • There are currently no refbacks.

Copyright (c) 2014 Ismail Mohd

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2005-2019 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website.