向量映射标量化函数的性质与向量优化问题解的存在性

摘要

在拓扑向量空间上定义一类向量映射的标量化函数,得到标量化函数与向量映射的下(上)半连续性、凸性以及拟凸性的对应性质.并且利用标量化函数的性质得到向量优化问题弱有效解存在的充分条件.%A class of scalarization function for vector map was defined in topological vector space. Some corresponding properties of scalarization function and vector mapping such as lower (upper) semicontinu-ity, convexity, and quasi-convexity were obtained. Moreover, the sufficient condition for existence of weak efficient solution in vector optimization was obtained by using the properties of scalarization function.