Iq new method for solving equality path-constrained dynamic optimization problems is proposed that directly solves the associated high-index differential and algebraic equation (DAE) using the dummy derivative method. This method eliminates efficiency and error control problems associated with other numerical methods for; solving these problems. It is proved that equality path constraints can cause the dynamic optimization problem to contain high-index DAEs. Also presented are a set of theorems that use controllability arguments to state when the equality path-constrained dynamic optimization problem is feasible. Results from several numerical examples are discussed, including a large-scale chemical engineering example.