### Abstract

This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.

Original language | English |
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Pages (from-to) | 399-410 |

Number of pages | 12 |

Journal | Journal of Optimization Theory and Applications |

Volume | 135 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Dec 1 |

Externally published | Yes |

### Keywords

- 0-1 integer programming
- Branch and bound algorithms
- Fractional programming problems
- Global optimization
- Portfolio optimization

### ASJC Scopus subject areas

- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics

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## Cite this

Konno, H., Tsuchiya, K., & Yamamoto, R. (2007). Minimization of the ratio of functions defined as sums of the absolute values.

*Journal of Optimization Theory and Applications*,*135*(3), 399-410. https://doi.org/10.1007/s10957-007-9284-z