可变序结构下向量优化中的一个新非线性标量化函数及其应用  

A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures

作　　者：李飞[1] LI Fei(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《应用数学和力学》2020年第3期329-338,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11431004,11601248)。

摘　　要：在具有可变序结构的一般拓扑向量空间中定义了一个新的非线性标量化函数,讨论了该函数的主要性质.同时作为应用,通过该函数构造出了一族半范数和一类赋范线性空间,并在最后建立了该非线性标量化函数和半范数的上、下半连续性结论.In a topological vector space with variable ordering structures,a new nonlinear scalarization function was defined and its main properties were discussed.Meanwhile a family of semi-norms and a class of related normed linear spaces were constructed with this nonlinear scalarization function.Also the conclusions about upper,lower semi-continuity of this nonlinear scalarization function and the semi-norm function was established.

关 键 词：向量优化 可变序结构 Gerstewitz泛函 非线性标量化函数 半范数 半连续性 

分 类 号：O221.6[理学—运筹学与控制论]