An implicit function formulation for optimization of discretized index-1 differential algebraic systems.

A formulation for the optimization of index-1 differential algebraic equation systems (DAEs) is described that uses implicit functions to remove algebraic variables and equations from the optimization problem. The formulation uses the implicit function theorem to calculate derivatives of functions that remain in the optimization problem in terms of a reduced space of variables, allowing it to be solved with second-order nonlinear optimization algorithms. The formulation is shown to lead to more reliable solver convergence when compared with a full-space simultaneous formulation in challenging case studies involving a chemical looping combustion reactor. In a steady state simulation problem, the implicit function formulation solves 82 out of 100 instances, while the full space formulation solves only 42 out of 100 instances. In a dynamic optimization problem, the implicit function formulation solves 189 out of 200 instances, while the full space formulation solves only 152 out of 200 instances.