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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 879739, 10 pages
http://dx.doi.org/10.1155/2014/879739
Research Article

Global Optimization for the Sum of Concave-Convex Ratios Problem

1School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China
2Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, China
3College of Science, Shenyang Agricultural University, Shenyang, Liaoning 110866, China

Received 29 January 2014; Revised 10 April 2014; Accepted 10 April 2014; Published 13 May 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 XueGang Zhou and JiHui Yang. 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

This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.