### Abstract

This paper is concerned with an efficient algorithm for solving a convex-convex type quadratic fractional program whose objective function is defined as the ratio of two convex quadratic functions and whose constraints are linear. This is a typical nonconcave maximization problem with multiple local maxima. The algorithm to be proposed here is a combination of (i) the classical Dinkelbach approach, (ii) the integer programming approach for solving nonconvex quadratic programming problems and (iii) the standard nonlinear programming algorithm. It will be shown that an exact algorithm which is a combination of (i) and (ii) above can solve problems much larger than those solved by an earlier algorithm based on a branch and bound algorithm. It addition, the combination of (i)-(iii) can solve much larger problems within a practical amount of time.

Original language | English |
---|---|

Pages (from-to) | 241-255 |

Number of pages | 15 |

Journal | Journal of Optimization Theory and Applications |

Volume | 133 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 May 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Dinkelbach method
- Global optimization
- Integer programming
- Local search algorithms
- Nonconvex quadratic programming problems
- Nonlinear fractional programs
- Portfolio analysis

### ASJC Scopus subject areas

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

### Cite this

*Journal of Optimization Theory and Applications*,

*133*(2), 241-255. https://doi.org/10.1007/s10957-007-9188-y

**An efficient algorithm for solving convex-convex quadratic fractional programs.** / Yamamoto, Rei; Konno, H.

Research output: Contribution to journal › Article

*Journal of Optimization Theory and Applications*, vol. 133, no. 2, pp. 241-255. https://doi.org/10.1007/s10957-007-9188-y

}

TY - JOUR

T1 - An efficient algorithm for solving convex-convex quadratic fractional programs

AU - Yamamoto, Rei

AU - Konno, H.

PY - 2007/5/1

Y1 - 2007/5/1

N2 - This paper is concerned with an efficient algorithm for solving a convex-convex type quadratic fractional program whose objective function is defined as the ratio of two convex quadratic functions and whose constraints are linear. This is a typical nonconcave maximization problem with multiple local maxima. The algorithm to be proposed here is a combination of (i) the classical Dinkelbach approach, (ii) the integer programming approach for solving nonconvex quadratic programming problems and (iii) the standard nonlinear programming algorithm. It will be shown that an exact algorithm which is a combination of (i) and (ii) above can solve problems much larger than those solved by an earlier algorithm based on a branch and bound algorithm. It addition, the combination of (i)-(iii) can solve much larger problems within a practical amount of time.

AB - This paper is concerned with an efficient algorithm for solving a convex-convex type quadratic fractional program whose objective function is defined as the ratio of two convex quadratic functions and whose constraints are linear. This is a typical nonconcave maximization problem with multiple local maxima. The algorithm to be proposed here is a combination of (i) the classical Dinkelbach approach, (ii) the integer programming approach for solving nonconvex quadratic programming problems and (iii) the standard nonlinear programming algorithm. It will be shown that an exact algorithm which is a combination of (i) and (ii) above can solve problems much larger than those solved by an earlier algorithm based on a branch and bound algorithm. It addition, the combination of (i)-(iii) can solve much larger problems within a practical amount of time.

KW - Dinkelbach method

KW - Global optimization

KW - Integer programming

KW - Local search algorithms

KW - Nonconvex quadratic programming problems

KW - Nonlinear fractional programs

KW - Portfolio analysis

UR - http://www.scopus.com/inward/record.url?scp=34547240222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547240222&partnerID=8YFLogxK

U2 - 10.1007/s10957-007-9188-y

DO - 10.1007/s10957-007-9188-y

M3 - Article

VL - 133

SP - 241

EP - 255

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 2

ER -