### Abstract

In this paper, we introduce a class of minimization problems whose objective function is the composite of an isotonic function and finitely many ratios. Examples of an isotonic function include the max-operator, summation, and many others, so it implies a much wider class than the classical fractional programming containing the minimax fractional program as well as the sum-of-ratios problem. Our intention is to develop a generic "Dinkelbach-like" algorithm suitable for all fractional programs of this type. Such an attempt has never been successful before, including an early effort for the sum-of-ratios problem. The difficulty is now overcome by extending the cutting plane method of Barros and Frenk (in J. Optim. Theory Appl. 87:103-120, 1995). Based on different isotonic operators, various cuts can be created respectively to either render a Dinkelbach-like approach for the sum-of-ratios problem or recover the classical Dinkelbach-type algorithm for the min-max fractional programming.

Original language | English |
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Pages (from-to) | 581-601 |

Number of pages | 21 |

Journal | Journal of Optimization Theory and Applications |

Volume | 146 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 May 6 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Optimization Theory and Applications*,

*146*(3), 581-601. https://doi.org/10.1007/s10957-010-9684-3