In this paper, we propose new concepts of sharp minimality in set-valued optimization problems by means of the pseudo-relative interior, namely pseudo-relative \(\phi \)-sharp minimizers. Based on this notion of minimality, we extend the existence result of a unique minimum of uniformly convex real-valued functions proved by Zălinescu in [25] to vector-valued as well as set-valued maps. Additionally, we provide some existence results for weak sharp minimizers in the sense of Durea and Strugariu [9].

中文翻译：

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集值优化中伪相对尖锐极小值的存在

在本文中，我们通过伪相对内部，即伪相对\（\ phi \）-锐化最小化器，提出了集值优化问题中的最小极值的新概念。基于极小值的概念，我们将Zălinescu在[25]中证明的一致凸实值函数的唯一极小值的存在结果扩展到矢量值映射和集值映射。此外，我们从Durea和Strugariu [9]的意义上提供了弱尖锐最小化器的存在性结果。