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 Z.alinescu 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].