Abstract, Dynamic optimisation problems axe usually solved by transforming them to nonlinear programming (NLP) problems with either sequential or simultaneous approaches. However, both approaches can still be inefficient to tackle complex problems. In addition, many problems in chemical engineering have unstable components which lead to unstable intermediate profiles during the solution procedure. If the numerical algorithm chosen utilises an initial value formulation, the error from decomposition or integration can accumulate and the Newton iteration* then faiL On the other hand, by njiiigsmUhkŜ hooting or collocation, our algorithm has favorable numerical characteristics for both stable and unstable problems; by exploiting the structure of the resulting system, a stable and efficient decomposition algorithm results.'Here solution of this NLP formulation is considered through a reduced Hessian Successive Quadratk Programming (SQP) approach. The routine chosen for the decomposition of the system equations is CX)LDAE, in which the stable multipk shooting scheme is implemented. To address the mesh selection, we will introduce a new bilevd framework that wiD decouple the element placement from the optimal control procedure. We will also provide a proof for the connection of our algorithm and the calculus of variations.
This paper discusses numerical issues in
differential−algebraic equation (DAE) optimization
concerning the stability and accuracy of the discretized nonlinear
programming problems (NLP).
First, a brief description of the solution strategy based on
reduced-Hessian successive quadratic
programming (rSQP) is presented, focusing on the decomposition step of
the DAE constraints.
Next, some difficulties associated with unstable DAE problem
formulations are exposed via
examples. A new procedure for detecting ill-conditioning and
problem reformulation is then
presented. Furthermore, some properties of this procedure as well
as its limitations are also
discussed. Numerical examples are provided, including a flowsheet
optimization problem with
an unstable reactor.
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