【摘要】 本文利用Minkowski型非线性标量化泛函分别建立了一般实线性空间中基于相对代数内部与向量闭包,实拓扑线性空间中基于相对拓扑内部与拓扑闭包,以及实分离局部凸拓扑线性空间中基于拟相对内部与拓扑闭包的非线性分离定理.这些新的分离定理能够用于研究序锥的拓扑内部甚至是相对拓扑内部或相对代数内部可能为空的向量优化问题.作为其应用,本文给出了向量优化问题相应弱有效解的一些非线性标量化性质;此外,也提出了无限维空间中的一些具体例子来对主要结果进行了解释.更多还原

【Abstract】 By means of the Minkowski-type nonlinear scalarization functional,in this paper,we establish some nonlinear separation theorems via relative algebraic interior and vector closure in a general real linear space,via relative topological interior and topological closure in a real topological linear space and via quasi relative interior and topological closure in a real separated locally convex topological linear space,respectively.These new separation theorems can be applied to study those vector optimization problems with the ordering cones having possibly empty topological interior and even relative topological interior or relative algebraic interior.As their applications,we give some nonlinear scalarization characterizations of the corresponding weak efficient solutions of vector optimization problems.Moreover,we also present some concrete examples to illustrate the main results in some infinite dimensional spaces.更多还原