【摘要】 在一种集合偏序关系下提出了集值映射的标量锥拟凸概念,讨论了它与各种锥凸性的关系.然后对恰当锥拟凸性得到了某种水平集意义下的刻画.同时建立了集值映射的各种锥凸性通过实值单调增加凸函数表示的标量化复合法则.最后给出了利用Gerstewitz泛函表示的对集值映射的锥拟凸性的标量化刻画.更多还原

【Abstract】 In this paper,we firstly introduce the notion of scalar cone-quasiconvexity for set-valued maps and discuss the relationships among several cone-convexities.A characterization for proper cone-quasiconvexity of set-valued maps is also given in the sense of a type of level set.Meanwhile,the composition rule of cone-convexity of set-valued maps is established by scalar increasing convex functions.We obtain a characterization for cone-quasiconvexity of set-valued maps by Gerstewitz functional finally.更多还原