## Abstract

In this paper, we extend the Dinkelbach-type algorithm of Crouzeix, Ferland, and Schaible to solve minmax fractional programs with infinitely many ratios. Parallel to the case with finitely many ratios, the task is to solve a sequence of continuous minmax problems, P(α_{k})=min _{x∈X}(max_{t∈T}[f_{t}(x)- α_{k}g_{t}(x)]), until {α_{k}} converges to the root of P(α)=0. The solution of P(α _{k} ) is used to generate α _{k+1}. However, calculating the exact optimal solution of P(α_{k} ) requires an extraordinary amount of work. To improve, we apply an entropic regularization method which allows us to solve each problem P(α _{k} ) incompletely, generating an approximate sequence {α̃_{k}}, while retaining the linear convergence rate under mild assumptions. We present also numerical test results on the algorithm which indicate that the new algorithm is robust and promising.

Original language | English |
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Pages (from-to) | 323-343 |

Number of pages | 21 |

Journal | Journal of Optimization Theory and Applications |

Volume | 126 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 Aug 1 |

## All Science Journal Classification (ASJC) codes

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