ransmission power. Since the power transmitted to user Cn,i on RB m is Pn, i(m) the total power is This total can be minimized by minimizing the power to each qualified user subject to the constraint that each QU remains qualified - i.e. it still has sufficient sSINR to meet the QoS objective. However, there is an additional constraint in that the received power (at the mobile ter- minal) PR. on RB m for user c n , must be above a certain value pR. min for satisfactory detection and the relationship between received power and transmitted power is given as From this it is clear that the optimization needs to maximize the number of users that are qualified, yet at the same time minimize the power as expressed above; this is a multifunc- tion optimization problem with the variables being the RB allocation and the power. One general approach for solving multi-objective optimization problems is to combine the individual objective functions into a single composite function such as the weighted sum method [47]. This is simple yet probably the most widely used classical approach but 8 Network Slicing with Spectrum Sharing does suffer from the need to find suitable weights and can be difficult to specify when one objective is to be maximized and another minimized. The authors in [48] carried out a very comprehensive survey of multi-objective optimization methods and came up with a helpful concluding remark: "In general, multi-objective optimization requires more computational effort than single-objective optimization. Unless preferences are irrelevant or completely under- stood, solution of several single objective problems may be necessary to obtain an acceptable final solution." This separation into separate phases was the approach adopted in Yang et al. [49]: that work did not include sharing between slices as the interest was only in the overall power. However, a scenario where users "belong" to different slices could be considered as the slice owning a user has no effect on the power allocation. Phase 1 is the alloca