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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 103569, 7 pages
http://dx.doi.org/10.1155/2014/103569
Research Article

Global Optimization for a Class of Nonlinear Sum of Ratios Problem

1Basic Course Department, Henan Mechanical and Electrical Engineering College, Xinxiang 453003, China
2College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received 5 November 2013; Revised 6 February 2014; Accepted 8 February 2014; Published 3 April 2014

Academic Editor: Baocang Ding

Copyright © 2014 Li Jin and Xue-Ping Hou. 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 present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in financial optimization, but the global optimization algorithm for this problem is still rare in the literature so far. In the algorithm we presented, the branch and bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of this problem belong. Convergence of the algorithm is shown. At last, some numerical examples are given to vindicate our conclusions.