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The differential-algebraic equation (DAE) optimization problem is transformed to a nonlinear programming problem by applying collocation on finite elements. The result- ing problem is solved using a reduced space successive quadratic programming (rSQP) algorithm. Here, the variable space is partitioned into range and null spaces. Partition- ing by choosing a pivot sequence for an LU factorization with partial piuoting allows us to detect unstable modes in the DAE gstem, which can now be stabilized without imposing new boundary conditions. As a result, the range .space is decomposed in a single step by exploiting the overall sparsity of the collocation matrix; which perjoims better than the two-step condensation method used in standard collocation solcers. To deal with ill-conditioned constraints, we also extend the rSQP algorithm to include dogleg steps for the range space step that solves the collocation equations. The per- formance of this algorithm was tested on two well known unstable problems and on three chemical engineering examples including two reactive distillation columns and a plug-frow reactor with free radicals. One of these is u batch column where an equilih- rium reaction takes place. The second reactiue distillation problem is the srartiip qf a continuous column with competitive reactions. These optimization problems, which in- clude more than 150 DAEs, ure solved in less than 7 CPU minutes on workstation class computers.

@article{ Cervantes1998, abstract = {The differential-algebraic equation (DAE) optimization problem is transformed to a nonlinear programming problem by applying collocation on finite elements. The result- ing problem is solved using a reduced space successive quadratic programming (rSQP) algorithm. Here, the variable space is partitioned into range and null spaces. Partition- ing by choosing a pivot sequence for an LU factorization with partial piuoting allows us to detect unstable modes in the DAE gstem, which can now be stabilized without imposing new boundary conditions. As a result, the range .space is decomposed in a single step by exploiting the overall sparsity of the collocation matrix; which perjoims better than the two-step condensation method used in standard collocation solcers. To deal with ill-conditioned constraints, we also extend the rSQP algorithm to include dogleg steps for the range space step that solves the collocation equations. The per- formance of this algorithm was tested on two well known unstable problems and on three chemical engineering examples including two reactive distillation columns and a plug-frow reactor with free radicals. One of these is u batch column where an equilih- rium reaction takes place. The second reactiue distillation problem is the srartiip qf a continuous column with competitive reactions. These optimization problems, which in- clude more than 150 DAEs, ure solved in less than 7 CPU minutes on workstation class computers.}, author = {Cervantes, A and Biegler, L T}, doi = {10.1002/aic.690440505}, file = {:Users/jboisvert/Library/Application Support/Mendeley Desktop/Downloaded/Cervantes - 1998 - Large‐scale DAE optimization using a simultaneous NLP formulation.pdf:pdf}, issn = {00011541}, journal = {AIChE Journal}, number = {5}, pages = {1038--1050}, publisher = {Wiley Subscription Services, Inc., A Wiley Company}, title = {{Large-scale DAE optimization using a simultaneous NLP formulation}}, url = {http://doi.wiley.com/10.1002/aic.690440505}, volume = {44}, year = {1998} }

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