### Table 1: Numberofiterations required to nd an optimal solution using the previous solution as a starting

2001

"... In PAGE 24: ... When a new user enters the system, running the MFVA algorithm using as astarting point the optimal solution for the problem prior to the new user apos;s arrival typically results in substantial computational savings. Table1 shows results from a power control problem involving a system of ten bytencells and approximately nine hundred mobile users. The number of iterations required to nd the optimal solution for an initial problem is given, along with the numberofiterations required to nd the optimal solution when additional users enter the system.... ..."

Cited by 10

### Table 1: Number of iterations required to nd an optimal solution using the previous solution as a starting point and using the vector (0; : : : ; 0) as a starting point.

2001

"... In PAGE 24: ... When a new user enters the system, running the MFVA algorithm using as a starting point the optimal solution for the problem prior to the new user apos;s arrival typically results in substantial computational savings. Table1 shows results from a power control problem involving a system of ten by ten cells and approximately nine hundred mobile users. The number of iterations required to nd the optimal solution for an initial problem is given, along with the number of iterations required to nd the optimal solution when additional users enter the system.... ..."

Cited by 10

### Table 1: Global optimal solution for different problem settings Exp

"... In PAGE 5: ... This information can be used as a base line to evaluate the performance of the proposed heuristics, as we will see in the following experiments. Three different sets of experiments are conducted as shown in Table1 . In all experiments, the time-varying observations on the different zones were generated randomly following a uniform distribution U(0,200).... In PAGE 5: ... Sensors reliability is assumed to be fixed with time and no lifespan loss associated with their moves. As expected and as shown in Table1 , the algorithm running time increases with the increase in number of zones, number of sensing sensors and length of the monitoring period. For example, in the first set of experiments, increasing the number of zones from 10 to 30 results in a jump in the solution running time from 1542.... ..."

### 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.... ..."

Cited by 16

### Table 12: Global solutions for Example 3

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

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 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 21: Solutions for Example 6, global solution postulated

1995

"... In PAGE 22: ... Notice that as one proceeds down the column (tray 2 is at the top of the column), the cpu times and number of iterations increase, indicating that the most di cult trays lie at the lower end of the column. Table21 shows the results when the solution corresponding to a global minimum of the Gibbs free energy function is used to generate the tangent plane distance function. The global solutions on all ve trays are LLV solutions.... In PAGE 22: ... The stability test for the ideal vapor phase obviously yields a nonnegative global solution in all cases. Therefore, because the only phase types considered are ideal vapor and liquid phases that can be described by the UNIQUAC equation, this means that it can be de nitively asserted that the solutions shown in Table21 are the equilibrium ones. Note that the fathoming rate remains high.... ..."

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### Table 3: errors for Problem 2, adaptive sparse grid accuracy P

1998

"... In PAGE 5: ... In Figure 3 the exact solution of Problem 2 together with an associated adaptive sparse grid is given. The results for adaptive sparse grids are given in Table3 . Here, the quotients must be viewed in a sense of \accuracy versus work involved quot;.... ..."

Cited by 1

### Table 8: Global solutions for Example 3, Conditions (ii)

1995

"... In PAGE 15: ... With a one phase solution postulated, there were no failures by the local solver in predicting instability although the global solution to the stability problem was only obtained 31 times out of 100 randomly selected starting points. Table8 shows the results for Condition (ii) where the di culty of the problem is re ected in the increased computer time required to establish stability. There were also a large number of failures (60 out of 100) when the stability problem was solved locally using MINOS5.... ..."

Cited by 18