Search of the global minimum by the method of exact quadratic regolarization

Authors

  • Анатолий Иванович Косолап Ukrainian University of Chemical Engineering Gagarina 8, Dnipropetrovsk, Ukraine, 49005, Ukraine

DOI:

https://doi.org/10.15587/2313-8416.2014.32250

Keywords:

global minimum, exact quadratic regularization, primal-dual interior point methods, dichotomy

Abstract

We offer a new method of exact quadratic regularization for search of a global minimum the functions with constraints. The method includes nonlinear transformations of the functions, local search and a dichotomy. This method has allowed to solve set of difficult test and applied problems of global optimization. Comparative numerical experiments have shown that new method is the best for the solution of this class of problems.

Author Biography

Анатолий Иванович Косолап, Ukrainian University of Chemical Engineering Gagarina 8, Dnipropetrovsk, Ukraine, 49005

Professor

Department of Specialized Computer Systems

References

Samarski, А. А., Mikhajlov, A. P. (2001). Mathematical modelling: Ideas, methods, examples. The second edition corrected. Moscow: Physmathlit, 320.

Kenneth, V. P., Storn, R. M., Lampinen, J. A. (2005). Differential Evolution. A Practical Approach to Global Optimization. Berlin: Springer-Verlag, 542.

Nocedal, J., Wright, S. J. (2006). Numerical optimization. Springer, 685.

Kosolap, A. (2013). Methods of Global Optimization. Dnipropetrovsk, Ukraine: Science and education, 316.

Ye, Y. (2003). Semidefinite programming. Stanford University, 161.

Floudas, C. A., Pardalos, P. M. (1990). A collection of Test Problems for Constrained Global Optimization Algorithms. Berlin Helldelberg: Springer-Verlag, 193.

Published

2014-12-25

Issue

Section

Physics and mathematics