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Center for Nonlinear Studies |
Nonlinear local optimization (nonlinear programming) is an important tool for engineering research. In particular, nonlinear programs with discretized differential-algebraic equation (DAE) systems as equality constraints can be used to determine optimal operating decisions with solve times that have the potential to be used in real-time applications. However, these optimization problems are often difficult to construct, analyze, and converge. This seminar presents three recent projects that have the goal of alleviating these difficulties in the context of a chemical looping combustion reduction reactor modeled with IDAES and Pyomo DAE. We first automatically identify differential and algebraic subsystems of the discretized model and identify causes of structural and numeric singularity using algorithms from graph theory. We then analyze the stability of our PDE discretization using newly introduced utilities in the Pyomo platform. Finally, we present an implicit function formulation for optimization of the discretized model that yields more reliable solver convergence, solving 50% more problem instances without an increase in solve time.
Host: Carleton Coffrin