An Algorithm for Global Optimization Using Formula Manupulation

Affiliation(s)

Department of Computer and Information Engineering, Nippon Institute of Technology, Saitama, Japan.

Division of Integrated Sciences, J. F. Oberlin University, Tokyo, Japan.

Department of Computer and Information Engineering, Nippon Institute of Technology, Saitama, Japan.

Division of Integrated Sciences, J. F. Oberlin University, Tokyo, Japan.

Abstract

Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively; this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments.

Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively; this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments.

Cite this paper

T. Shohdohji and F. Yano, "An Algorithm for Global Optimization Using Formula Manupulation,"*Applied Mathematics*, Vol. 3 No. 11, 2012, pp. 1601-1606. doi: 10.4236/am.2012.311221.

T. Shohdohji and F. Yano, "An Algorithm for Global Optimization Using Formula Manupulation,"

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