锥广义类凸集值映射的择一性定理及应用

Theorem of Alternative for Cone Generalized Convexlike Set-valued Maps and It's Applications

将单值映射的锥广义类凸概念拓广到集值映射,引入了集值映射的锥广义类凸性,然后建立了一个择一性定理,并借助它导出了锥广义类凸集值映射优化问题的标量化结果和Lagrange乘子定理。

By extending the concept of cone generalized convexlikeness of single-valued maps,it first introduce cone generalized convexlikeness of set-valued maps,and then give a theorem of the alternative.Furthermore,scalarization result and Lagrange multiplier theorem are established by using the alternative theorem.