中文摘要：

将赋范线性空间中增广对偶锥的概念推广到局部凸空间中，在两种情形下分别给出了广义增广对偶锥的定义．然后讨论了它们的主要性质，并在合适的假设下建立了广义增广对偶锥非平凡的存在性条件．

英文摘要：

In this paper, the notions of augmented dual cones are extended from normed linear spaces to locally convex spaces. The extended augmented dual cones are defined respectively in two cases. Then we discuss their main properties, and also establish existence conditions of nontriviality of the extended augmented dual cones under suitable hypothesis.