### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Optimization Theory and Applications*,

*135*(3), 399-410. https://doi.org/10.1007/s10957-007-9284-z

**Minimization of the ratio of functions defined as sums of the absolute values.** / Konno, H.; Tsuchiya, K.; Yamamoto, Rei.

Research output: Contribution to journal › Article

*Journal of Optimization Theory and Applications*, vol. 135, no. 3, pp. 399-410. https://doi.org/10.1007/s10957-007-9284-z

}

TY - JOUR

T1 - Minimization of the ratio of functions defined as sums of the absolute values

AU - Konno, H.

AU - Tsuchiya, K.

AU - Yamamoto, Rei

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

KW - 0-1 integer programming

KW - Branch and bound algorithms

KW - Fractional programming problems

KW - Global optimization

KW - Portfolio optimization

UR - http://www.scopus.com/inward/record.url?scp=36148997292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36148997292&partnerID=8YFLogxK

U2 - 10.1007/s10957-007-9284-z

DO - 10.1007/s10957-007-9284-z

M3 - Article

AN - SCOPUS:36148997292

VL - 135

SP - 399

EP - 410

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 3

ER -