## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014 (2014), Article ID 490297, 10 pages.

### A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients

Hongwei Jiao and Yongqiang Chen

#### Abstract

A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.

#### Article information

**Source**

J. Appl. Math., Volume 2014 (2014), Article ID 490297, 10 pages.

**Dates**

First available in Project Euclid: 2 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425305637

**Digital Object Identifier**

doi:10.1155/2014/490297

**Mathematical Reviews number (MathSciNet)**

MR3191120

**Zentralblatt MATH identifier**

07010653

#### Citation

Jiao, Hongwei; Chen, Yongqiang. A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients. J. Appl. Math. 2014 (2014), Article ID 490297, 10 pages. doi:10.1155/2014/490297. https://projecteuclid.org/euclid.jam/1425305637