Numerical Optimization of a Simulated Moving Bed Process using a Total quasi-Newton Approach
The CUTEr test set is often used to verify the robustness and performance of non-linear optimization solvers. In our experiments it was observed that the total quasi-Newton solver LRAMBO achieves no reduction/improvement when contstraint Jacobians are cheap to evaluate and easy to factorize, which is true for practically all problems in the CUTEr test set. This makes the use of optimization algorithms exclusively based on low rank updates and evaluating derivative vectors somewhat slower than other methods on this test set. In contrast, non-linear optimization tools using exact sparse derivative matrices and sparse linear algebra usually perform better. In this paper we focus on a Simulated Moving Bed process. Based on fluid-solid interactions, this system never reaches steady state, but a cyclic steady state, which leads to dense Jacobians of the constraints, whose computation dominates the overall cost of the optimization strategy. After a detailed investigation of the SMB problem structure we present some optimal solutions and run-times obtained by LRAMBO that encourage dense non-linear optimization solvers for a certain class of problems.