This paper considers the optimization of transient systems consisting of a fixed number of stages, each of which is described by an index-1 system of differential-algebraic equations (DAE). General initial conditions at the start of the first stage and junction conditions between stages are allowed, as well as point equality and inequality constraints at the end of each stage. A control vector parametrization approach is used to convert the above problem to a finite dimensional nonlinear programming (NLP) problem. The function gradients required for the solution of the NLP are calculated through the solution of a multistage DAE system in the variable sensitivities.