| 区间值函数的可微性及其在区间值规划中的应用 |
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| 引用本文： | 包玉娥,李娜,张林芬. 区间值函数的可微性及其在区间值规划中的应用[J]. 数学研究及应用, 2020, 40(4): 415-431 |
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| 作者姓名： | 包玉娥 李娜 张林芬 |
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| 作者单位： | 内蒙古民族大学数学学院, 内蒙古 通辽 028043 |
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| 基金项目： | 国家自然科学基金(Grant No.11461052),内蒙古自然科学基金(Grant No.2018MS01010). |
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| 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.
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| 关 键 词： | 区间值函数 $D$-可微性 区间值规划 KKT最优条件 |
| 收稿时间： | 2019-02-20 |
| 修稿时间： | 2020-04-21 |
Differentiability of Interval Valued Function and Its Application in Interval Valued Programming |
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| Yu-e BAO,Na LI,Linfen ZHANG. Differentiability of Interval Valued Function and Its Application in Interval Valued Programming[J]. Journal of Mathematical Research with Applications, 2020, 40(4): 415-431 |
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| Authors: | Yu-e BAO Na LI Linfen ZHANG |
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| Affiliation: | College of Mathematics and Physics, Inner Mongolia University for Nationalities, Inner Mongolia 028043, P. R. China |
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| Abstract: | 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. |
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| Keywords: | interval-valued function $D$-differentiability interval-valued programming KKT optimal condition |
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