一类不可微广义分式规划的K-T型必要条件

K-T Type Necessary Conditions for a Class of Nondifferentiable Minimax Fractional Programming

本文对一类在Rn的开子集X上的非线性不等式约束的广义分式规划问题: 目标函数中的分子是可微函数与凸函数之和而分母是可微函数与凸函数之差,且约束函数是可微的,在Abadie约束品性或Calmness约束品性下,给出了最优解的Kuhn-Tucker 型必要条件,所得结果改进和推广了已有文献中的相应结果．

The Kuhn-Tucker type necessary optimality conditions are given for the problem of minimizing a maxmum fractional function~ where the numerator of the function involved is the sum of a differentiable function and a convex function while the denominator is the difference of a differentiable function and a convex function, subject to a set of differentiable nonlinear inequalities on an open subset X of R^n, under the conditions of the Abadie constraint qualification or the calmness constraint qualification. The results obtained improve and extend some of the existing results in the literature.