单调Minkowski泛函与Henig真有效性的标量化

Monotone Minkowski Functionals and Scalarizations of Henig Proper Efficiency

没有凸锥的闭性和点性假设,该文考虑由一般凸锥生成的单调Minkowski泛函并研究其性质.由此,在偏序局部凸空间的框架下,通过利用单调连续Minkowski泛函和单调连续半范,该文分别获得了一般集合及锥有界集合的弱有效点的标量化.利用此弱有效性的标量化,该文分别推导出一般集合及锥有界集合的Henig真有效点的标量化.进而,当序锥具备有界基时,该文获得局部凸空间中超有效性的一些标量化结果.最后,该文给出Henig真有效性和超有效性的稠密性结果.这些结果推广并改进了有关的已知结果.

Without the closedness and the pointedness of convex cones, we consider monotone Minkowski functionals generated by general convex cones and investigate properties of those Minkowski functionals. From this, in the framework of partially ordered locally convex spaces we obtain scalarizations of weakly efficient points of a general set and of a cone-bounded set by using a monotone continuous Minkowski functional and a monotone continuous semi-norm, respectively. Using the scalarizations of weak efficiency, we deduce scalarizations of Henig properly efficient points of a general set and of a cone-bounded set, respectively. Moreover, when the ordering cone has a bounded base, we obtain some scalarization results on superefficiency in locally convex spaces. Finally we give some density results for Henig proper efficiency and superefficiency. These results generalize and improve the related known results.