All mathematical models contain parameters that must be determined for the model to represent accurately the behavior of the system. The parameter estimation problem is usually solved as an unconstrained optimization problem independent of the model equations. However, by integrating the parameter estimation problem with the generation of the model’s state profiles, constraints can be embedded directly into the optimizer, and an infeasible path solution approach can be used. Nonlinear programming is the ideal framework for formulating constrained optimization problems. The model is introduced into this framework as constraints using orthogonal collocation on finite elements. The resulting nonlinear programming problem is then solved using sequential quadratic programming. We demonstrate this approach on a mathematical model of a proton-exchange-membrane fuel cell in which four parameters are estimated and nine states’ profiles are determined.