Nonconvex Separation Functional in Linear Spaces with Applications to Vector Equilibria
在未赋予拓扑结构的实线性空间中研究非凸分离泛函，利用代数内点和代数闭包推导其性质，并通过标量化方法刻画向量均衡问题的弱有效解。
In this paper, the so-called nonconvex separation functional is studied in a real linear space not necessarily endowed with a topology. The essential properties of this functional, which are well known in the topological framework, are derived by using algebraic counterparts to the topological concepts of interior and closure. Finally, it is used to characterize, in the same algebraic setting and by scalarization, weak efficient solutions of vector equilibrium problems defined through algebraic solid ordering sets.