E-预不变凸区间值函数及其在数学规划中的应用

E-Preinvex Interval-Valued Function and Its Application in Mathematical Programming

【目的】提出并研究了在LU-序关系下的E-预不变凸区间值函数。【方法】首先给出了LU-E-预不变凸区间值函数和LU-E-不变凸区间值函数的定义,举例验证了LU-E-预不变凸区间值函数的存在性;其次讨论了LU-E-预不变凸区间值函数与其他几类区间值函数间的关系;最后研究了一类LU-E-预不变凸区间值优化问题,给出了E-type-Ⅰ型最优解和E-type-Ⅱ型最优解的概念,并证明了E-KKT最优性条件的必要性和充分性条件。【结果】基于LU-序关系,理论推导并举例验证。【结论】文中将近期关于广义凸函数的一些研究成果进行了推广,在一定程度上丰富了广义凸函数的研究。

[Purposes]Here it mainly studies the correlation properties of LU-E-preinvex interval-valued function under LU-order relations and its application in mathematical programming.[Methods]On the basis of order relations,the theory is deduced and verified with examples.[Findings]Firstly,the definition of the LU-E-preinvex interval-valued function and the LU-E-convex interval value function is given.And the existence of the LU-E-preinvex interval-valued function is verified by example.Secondly,the relationship between LU-E-preinvex interval-valued function and other interval valued functions is discussed.Finally,the LU-Epreinvex interval-valued optimization problem is studied and the concept of E-type-Ⅰ optimal solution and the E-type-Ⅱ optimal solution for generalized convex interval-valued optimization problems is given.And it proved that the E-KKT optimality conditions of necessity and sufficiency conditions.[Conclusions]Some recent research results on generalized convex functions are generalized,which enriches the research on generalized convex functions to some extent.