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

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.