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7.5 Hybrid Filter Trust-region Algorithm Table 7.10: Perturbation results with FOC Optimal value 300 40 35 160.97 160.97 14.87 14.87 CO2 purity∗ 303 50.16% 39 49.83% 33 50.04% 163.97 50.6% 157.97 48.44% 15.87 52.21% 13.87 47.94% CO2 recovery∗ 97.26% 97.72% 97.31% 96.69% 97.56% 95.12% 98.26% Perturbed value Ph (kPa)† Pl (kPa)† tp (sec)† ta (sec) ta (sec) ua (cm/s) ua (cm/s) ∗Optimal CO2 recovery: 97.19%, CO2 purity: 50.01%, †at bound obtained from ROM-based optimization in AMPL, and rigorous model simulation in MATLAB. Such a comparison in Figure 7.4 reveals convincing behavior of the reduced-order model as the profiles are nearly identical. 7.5 Hybrid Filter Trust-region Algorithm 7.5.1 Motivation In this section we develop a hybrid filter-based trust-region algorithm for optimization involving ROMs. The algorithm is hybrid in the sense that it utilizes both ZOC and FOC at different times during its course. The motivation to develop this algorithm comes from two key observations in the aforemen- tioned PSA case study. First, we notice that although ROM-based trust-region subproblems with ZOC cannot ensure convergence to an optimal point, they are at least capable of generat- ing descent directions and even attain feasibilty even without the actual gradient information. Moreover, constructing FOC for every trust-region iteration is expensive as it involves compu- tation of gradients from the original problem. However, FOC is necessary to converge to an optimal point. Therefore, we propose a hybrid strategy in which the trust-region algorithm be- gins with subproblems constructed with ZOC. This is continued until no further improvement is observed, after which the algorithm switches to subproblems with FOC until convergence. Second, we observe in the optimization case study with FOC that the penalty-based trust- Chapter 7. Trust-region Framework for ROM-based Optimization 162PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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