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A nested, simultaneous approach for dynamic optimization problems .1.
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DOI：10.1016/0098-1354(95)00206-5.png)
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Process engineering provides a wealth of applications for dynamic optimization problems. To address these problems, we present a simultaneous approach for optimization of process models described by differential/algebraic equations by discretizing the variables through collocation on finite elements. By using Radau collocation, the algorithm has favorable stability properties for high index problems and 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 Quadratic Programming (SQP) approach, where linearized state variables are eliminated and reduced quadratic programming (QP) subproblems update the control variables. Although this paper primarily addresses fixed element problems, we also briefly describe a new framework to determine the element placement and addition via bilevel optimization. These approaches will be demonstrated through small process examples.
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