### Table 12. Local and global solutions

### Table 8: Global Solution for Example 1

in Global Optimization For The Phase And Chemical Equilibrium Problem: Application To The NRTL Equation

1995

"... In PAGE 31: ... The number of connected variables is then given as: NCV = jCj jPj ? r = 2 2 ? 2 = 2 Thus, a maximum of 22 = 4 relaxed dual subproblems must be solved at each iteration. From a starting point in the center of the feasible region, the GOP algorithm converges to the global solution in 7 iterations, and the solution is given in Table8 . From this initial point, a local solver may be unable to nd the global solution.... ..."

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### Table 2: the list of consistent and compatible global solutions

2002

"... In PAGE 27: ... The matches resulting from the composition of all pairs of mutually consistent and compatible local solutions are shown in Table 2. Table2 : the list of consistent and compatible global solutions, approximately here Redundant global solution GS0 is eliminated. The delay associated with each global solution is compared with the one expected from the currently implemented control.... In PAGE 41: ... 41 List of Figures Figure 1: the distributed architecture in CARTESIUS (11) Figure 2: The agent internal structure (14) Figure 3: the location of the incident, the major routes on the network, and the control devices used by CARTESIUS (24) Figure 4: the construction of the search tree in the example (25) List of Tables Table 1: the strategies and control actions developed by the agents (25) Table2 : the list of consistent and compatible global solutions (27) Table 3: final global solution (27) List of Keywords Incident management Decision support Distributed problem solving Functionally Accurate Cooperation Traffic control ... ..."

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### Table 10: Global solutions for Example 4

1995

"... In PAGE 20: ...function. If the trivial solution is tested for stability, Table10 gives the resulting chemical potentials, while Figure 5 shows the objective function as a nonconvex curve that represents the tangent plane distance function for this case. Note that there is a local maximum of zero at y1 0:5, but this is the largest value the objective function takes.... In PAGE 20: ... This will not be the case in general, where the global solution of the stability problem may be the only stationary point with a negative distance.If the postulated solution is the global LL solution, which is also given in Table10 , then the tangent plane distance function will be nonnegative everywhere, and this is shown in Figure 5. Again it is a nonconvex curve, and the branch and bound algorithm correctly identi es the global solution in 62 iterations, with the GOP algorithm consuming a total time of 0.... In PAGE 20: ...35 cpu sec. The global solutions of the stability problem for both these cases are given in Table10 , along with the usual computational results. The iteration at which the tangent plane distance function becomes negative occurs very early, re ecting behavior already seen in the case of the NRTL equation.... ..."

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### Table 16: Global solution for Example 5

in Global Optimization For The Phase And Chemical Equilibrium Problem: Application To The NRTL Equation

1995

"... In PAGE 33: ... ^ GII de ned the objective function that was minimized and NCV = 3. The global solution for the feed charge under consideration is supplied in Table16 . The water rich phase composes 52% of the top phase separator exit stream.... ..."

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### Table 10: Global solution for Example 2

in Global Optimization For The Phase And Chemical Equilibrium Problem: Application To The NRTL Equation

1995

"... In PAGE 32: ... (9) will be used. The feed charge is given in Table10 . No reaction occurs so that the rank of the material balance matrix is given by the number of components.... In PAGE 32: ... A total of 461 relaxed dual subproblems were solved and the percentage of total fathomed solutions was 82%. The optimal solution is given in Table10 , featuring a toluene-rich phase and a water-rich phase. When the stability problem (S) was solved using this global solution, it was found to be stable with respect to the incipient vapor phase.... ..."

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### Table 12: Global solutions for Example 3

1995

"... In PAGE 32: ... Walraven and van Rompay [63] subsequently used this problem in order to test their phase splitting algorithm for a number of di erent feed charges. Two source feeds from the work of Walraven and van Rompay [63] were examined, and these charges are given in Table12 . The rst of these lies well within the immiscibility region { fnT i g = f0:04; 0:16; 0:80g { and therefore causes little problem for a local solver.... ..."

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### Table 11: Global Solution for Example 5

1995

"... In PAGE 22: ... Table11 .... ..."

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### Table 4: Global solutions for Example 2

1994

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