A problem of load balancing in isolated DC microgrids is considered in this paper. Here, a DC load is fed by multiple heterogeneous DC sources, each of which is connected to the load via a boost converter. The gains of the DC Converters (DCC's) provide for a means to control the division of load current amongst the DC sources. The primary objective of the control scheme is to minimise the total losses in the network, while maintaining the output voltage within a desired range, serving the load current demand and adhering to VI-characteristics of the power sources. Under assumptions of concavity/monotonocity/piece-wise-linearity of the VI-characteristics, the problem is solved using a convex relaxation. It is shown that the solution to the relaxed problem is tight. Thus, the resulting algorithm is guaranteed to reach global optimality in a numerically efficient manner [1]. Simulations are provided for corroboration. © 2022 IEEE.