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Section II. This implies that ∂fR has an opposite sign in Section I during optimization which ∂tp gets corrected in Section II. Moreover, since Ph hit its upper bound and Section I terminates during same iteration (k = 34), we conclude that CO2 recovery improves in Section I even k ∂ fR with incorrect k due to the increment obtained in Ph. Another key observation is the 31st ∂tp iteration (k = 30) when we take a step despite ρk being negative. This is a consequence of the step 3(e) in the algorithm. In this iteration, although predk < 0, we observe aredk > 0. As highlighted before, once feasibility is attained in the exact penalty trust-region algo- rithm, we are not allowed a move which increases infeasibility. This eventually causes Algorithm I to pursue tiny steps towards optimum. In contrast, Algorithm II allows such a step which can increase infeasiblity when it tries to improve objective function value. For instance, in Table B.4, we notice iterations k=28, or 30, or iterations after k = 33, when algorithm sacrifices feasibility in order to achieve greater improvement in CO2 recovery. Hence, Algorithm II takes fewer iterations to optimum than Algorithm I. Table 7.11 lists the optimal values of the decision variables together with the optimization CPU time. With 52,247 algebraic variables, Algorithm II terminated within a reasonable CPU time of 1.36 hrs. As observed in the case of exact penalty trust-region algorithm with FOC, Ph, Pl, and tp are at their bounds at the optimum. However, the local optimum obtained in this case is slighly different from the one obtained in section 7.4.3.3 in the sense that the values of ta and ua are marginally different. As a consequence, optimal CO2 recovery obtained in this case is marginally better than the one obtained in section 7.4.3.3. We also report the purities and recoveries of nitrogen and CO2 obtained from AMPL after final optimization iteration, and from the rigorous model MATLAB simulation at the optimum. The values are fairly close with no appreciable difference. Table 7.12 lists the results for the pertubation analysis performed in order to validate if the algorithm terminated at an optimal point. A positive perturbation for Ph at its upper bound and a negative perturbation for tp at its lower bound improves both CO2 purity and recovery, while a negative perturbation for Pl at its lower bound improves recovery but deteriorates CO2 7.6 PSA Case Study Revisited Chapter 7. Trust-region Framework for ROM-based Optimization 180PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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