This paper presents a new approach to the solution of optimal control problems for which the system behaviour is described by a mixed set of differential-algebraic equations and inequalities. We first convert general inequalities to equations using slack variables, then use barrier functions to deal with the variable bounds and generate a smooth DAE system. We develop new necessary conditions of optimality for this system, which yield a two-point boundary-value problem, and describe a simple interior-point algorithm for solving this problem, which does not suffer an explosion in problem size as the number of variables increases or the discretization of the problem is refined. Numerical results are presented for several well known test problems and a larger problem involving optimal control of a typical process plant.