区间值函数的可微性及其在区间值规划中的应用

Differentiability of Interval Valued Function and Its Application in Interval Valued Programming

中文关键词:  区间值函数  $D$-可微性  区间值规划  KKT最优条件

英文关键词:interval-valued function  $D$-differentiability  interval-valued programming  KKT optimal condition

中文摘要:

      利用实值函数的全微分思想,讨论了区间值函数的可微性,建立了区间值函数的$D$-可微性的概念及其一些基本性质. 通过讨论无约束区间规划的最优性条件,给出了一类约束函数为实值函数的约束区间值规划问题取得最优解的必要条件. 同时给出了具有实值函数约束的凸区间值规划问题取得最优解的充分条件.

英文摘要:

      In this paper, the differentiability of interval valued function is discussed by using the idea of total differential of real valued function, the concept of $D$-differentiability of interval valued function is established and some basic properties are given. By discussing the optimality condition of unconstrained interval programming, the necessary conditions for obtaining the optimal solution of a class of constrained interval valued programming with real valued function constraints are given. Meanwhile, the sufficient conditions for obtaining the optimal solution are given for the convex interval value programming problem with real value function constraints.