A method to identify linear parameter varying models through minimisation of an -norm objective is presented. The method uses a direct nonlinear programming approach to a non-convex problem. The reason to use -norm is twofold. To begin with, it is a well-known and widely used system norm, and second, the cost functions described in this paper become differentiable when using the -norm. This enables us to have a measure of first-order optimality and to use standard quasi-Newton solvers to solve the problem. The specific structure of the problem is utilised in great detail to compute cost functions and gradients efficiently. Additionally, a regularised version of the method, which also has a nice computational structure, is presented. The regularised version is shown to have an interesting interpretation with connections to worst-case approaches.