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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 408918, 8 pages
http://dx.doi.org/10.1155/2014/408918
Research Article

Global Optimization for the Sum of Certain Nonlinear Functions

1Faculty of Engineering, Graduate School of Engineering, Mie University, Kurimamachiyamachi, Tsu 514-8507, Japan
2Department of Education, Mie University, Kurimamachiyamachi, Tsu 514-8507, Japan

Received 13 April 2014; Revised 19 August 2014; Accepted 20 August 2014; Published 10 November 2014

Academic Editor: Julio D. Rossi

Copyright © 2014 Mio Horai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend work by Pei-Ping and Gui-Xia, 2007, to a global optimization problem for more general functions. Pei-Ping and Gui-Xia treat the optimization problem for the linear sum of polynomial fractional functions, using a branch and bound approach. We prove that this extension makes possible to solve the following nonconvex optimization problems which Pei-Ping and Gui-Xia, 2007, cannot solve, that the sum of the positive (or negative) first and second derivatives function with the variable defined by sum of polynomial fractional function by using branch and bound algorithm.