不精确分式规划的一种有效算法

对于不精确分式规划，给出一个具有简单形式的等价规划以及一个参数规划．提出有关它们之间联系的一些基本理论，构造了通过求解参数规划来求解不精确规划的一簇算法．在一定的假设下，该簇算法的收敛速度至少是线性的．通过每次迭代中适当的选择参数可以得到具有全局收敛性的超线性算法，并且该簇算法在每次迭代时参数的取法有很大的灵活性，从而在求解时允许有较大的误差而无损于相应的收敛速度．

The efficient algorithm for inexact fractional programming

For an inexact fractional programming problem, an equivalent program of very simple form and a parametric program are presented. Some basic results for the relationship between a parametric program and the equivalent program are given. And a class of algorithms is proposed by solving the parameter program to solve the original inexact fractional program. The algorithms are convergent under mild assumptions, and converge at least linearly under the reasonable assumptions. The algorithms have a superlinear rate of convergence by choosing some of the parameters specially. The flexible choice of all the parameters also shows that the algorithms are stable concerning small perturbation of the parameters.