This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization ...This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.展开更多
关于线性分式函数 f（x）=（ax+b）/（cx+d）（ad≠bc）的 n 次迭代问题,用一般初等方法,只能对一些特殊的类型进行迭代,而对于一般的情形,用这类初等方法则很难求出迭代规律,对于不同线性分式函数 f<sub>i</sub>（x）=（a&...关于线性分式函数 f（x）=（ax+b）/（cx+d）（ad≠bc）的 n 次迭代问题,用一般初等方法,只能对一些特殊的类型进行迭代,而对于一般的情形,用这类初等方法则很难求出迭代规律,对于不同线性分式函数 f<sub>i</sub>（x）=（a<sub>i</sub>x+b<sub>i</sub>）/（c<sub>i</sub>+d<sub>i</sub>）（a<sub>i</sub>d<sub>i</sub>≠b<sub>i</sub>c<sub>i</sub>,i=1,2,…,n）的 n 次迭代 f<sub>n</sub>{f<sub>n-1</sub>[…f<sub>2</sub>（f<sub>1</sub>（x））…]},上述方法就更显得无能为力.本文用矩阵理论讨论了一般线性分式函数的迭代。展开更多
基金supported by the National Science Foundation of the United States under Grant No. #DMI- 0553310
文摘This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.
文摘关于线性分式函数 f（x）=（ax+b）/（cx+d）（ad≠bc）的 n 次迭代问题,用一般初等方法,只能对一些特殊的类型进行迭代,而对于一般的情形,用这类初等方法则很难求出迭代规律,对于不同线性分式函数 f<sub>i</sub>（x）=（a<sub>i</sub>x+b<sub>i</sub>）/（c<sub>i</sub>+d<sub>i</sub>）（a<sub>i</sub>d<sub>i</sub>≠b<sub>i</sub>c<sub>i</sub>,i=1,2,…,n）的 n 次迭代 f<sub>n</sub>{f<sub>n-1</sub>[…f<sub>2</sub>（f<sub>1</sub>（x））…]},上述方法就更显得无能为力.本文用矩阵理论讨论了一般线性分式函数的迭代。
