ONETEP is a linear scaling code for performing first-principles total energy calculations within density-functional theory (DFT). The method is based on the density-matrix formulation of DFT and involves the iterative minimization of the total energy with respect to a set of local orbitals and a density kernel. An overview is given of the kernel optimization methods proposed in the literature and implemented in ONETEP, focusing in particular on the constraints of compatibility, idempotency and normalization that must be applied. A method is proposed for locating the chemical potential which may be useful in applying the normalization constraint and analysing the electronic structure near the Fermi level.