Simultaneous strategies for optimization of differential-algebraic systems

Abstract: "A Simultaneous approach to the optimization of problems involving both Differential and Algebraic equation models (DAE) is developed. The equations that result from a discretization of a DAE model using orthogonal collocation on finite elements (OCFE), are incorporated directly into the optimization problem, and the combined problem is then solved using an efficient large-scale optimization strategy. In formulating this simultaneous strategy, profile constraints can be incorporated and handled automatically as part of the optimization problem. Moreover, since the DAE model is solved only once as the optimization problem converges, this approach can have a significant impact on the efficiency and reliability of the algorithm.To ensure accuracy of the solution of the Simultaneous strategy, reliable error estimates have been developed which not only permit an assessment of the validity of the results obtained, but also allow for an adaptive refinement of the mesh on which the solution is computed. Criteria which permit such estimates are discussed, and the concept of "equidistibution" is outlined.When control profiles are introduced, the error criteria become considerably more complicated. Here, we relate optimal control problems to the well-known index problem of DAE systems. A number of examples are presented that illustrate the difficulties of DAE systems and strategies are outlined for solving these problems. Finally, the Simultaneous strategy will be demonstrated on several optimization problems, which require determination of continuous, possibly constrained state profiles, as well as optimal parameter values and control profiles."