The traditional approach to finding the values of the parameters in differential or differential-algebraic models by feasible path optimization needs good initial estimates of the values and requires repeated numerical solution of the model equations. These shortcomings can be overcome by converging to the optimal values and to the solution to the model equations simultaneously via an infeasible path. The model equations are converted into algebraic constraints by orthogonal collocation and the resulting constrained minimization is solved by successive quadratic programming. This procedure is demonstrated on two problems and is shown to be both robust and computationally efficient.