Stereotactic Radiosurgery (SRS) is an effective technique for treating brain metastasis and non-invasive surgery. We discuss the application of the Constrained Convex Moment-based and Unconstrained Convex Moment-based (UCM) approaches, previously introduced for Intensity Modulated Radiotherapy treatment planning, to the so-called segment duration problem in SRS. Specifically, we focus on the segment duration optimization for the state-of-the-art Leksell Gamma Knife{\textregistered} Perfexion{\texttrademark} Elekta using UCM approach. In the latter formulation we consider the additional beam-on-time criterion to make the resulting treatment plan more preferable in terms of its delivery time. We will illustrate the preliminary performance results of this approach on anonymized data corresponding to three previously treated patient cases.