Differentiability of Interval Valued Function and Its Application in Interval Valued Programming
Received:February 20, 2019  Revised:April 21, 2020
Key Word: interval-valued function   $D$-differentiability   interval-valued programming   KKT optimal condition  
Fund ProjectL:Supported by the National Natural Science Fund of China (Grant No.11461052) and the Natural Science Foundation of Inner Mongolia (Grant No.2018MS01010).
Author NameAffiliation
Yu-e BAO College of Mathematics and Physics, Inner Mongolia University for Nationalities, Inner Mongolia 028043, P. R. China 
Na LI College of Mathematics and Physics, Inner Mongolia University for Nationalities, Inner Mongolia 028043, P. R. China 
Linfen ZHANG 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2020.04.009
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