### Table 3: Summary of the Experimental Results on Constrained Optimization.

"... In PAGE 34: ...Constrained Optimization We now turn to constrained optimization problems which are, in general, very di cult to solve. Table3 summarizes some of our computation results on some of the toughest problems from [10]. We give the number of variables in the initial statement (v), the number of constraints (c), the CPU time, and the number of splits.... ..."

### Table 6: Constrained Optimization for Minimum $/RPM

"... In PAGE 10: ...45 0.404 Desirability 0 1 Figure 14: Prediction Profiles: Constrained Optimization and Sensitivities The point design optimization results obtained for this example are summarized in Table6 and Table 7. Table 6 contains the optimal setting of the design variables while Table 7 lists the minimal value for the objective function, $/RPM, and the values for the constraints generated by the RSEs as well as the results of a verification run of FLOPS.... In PAGE 10: ...404 Desirability 0 1 Figure 14: Prediction Profiles: Constrained Optimization and Sensitivities The point design optimization results obtained for this example are summarized in Table 6 and Table 7. Table6 contains the optimal setting of the design variables while Table 7 lists the minimal value for the objective function, $/RPM, and the values for the constraints generated by the RSEs as well as the results of a verification run of FLOPS. The right hand column displays the difference of these two values indicating a percentage error for the RSE-based approach.... In PAGE 11: ... The fact that the constraint RSE was formed, however, provides the capability to have a truly noise- constrained vehicle once suppression can be accurately modeled. The optimum aerodynamic design variable settings from Table6 yield a wing planform illustrated in Figure 15. The figure on the right displays the location of the variables and their nominal values.... ..."

### Table 1: Results of the Constrained Optimization Problem

"... In PAGE 9: ...961.81381. The first two constraints are active at the optimum. Table1 provides the results obtained using a swarm size of 200 flying for 100 time steps and also with a swarm size of 300 flying for 100 time steps. Five successive trials have been conducted to compute the best, worst and the average values of the objective using the present algorithm.... In PAGE 9: ...he worst, average and the best values are [-6729.7983, -6837.4347, -6883.7124]. It can be clearly observed from Table 2 that our algorithm reports consistent values with much less evaluations when compared with Koziel and Michalewicz (1999). Table1 . Results of the Constrained Optimization Problem Table 2.... ..."

### Table 4 Summary of the experimental results on constrained optimization

### TABLE I Comparison of Results for the Two-Variable Constrained Optimization Problem.

1999

Cited by 2

### Table 2: Simulated annealing amp; genetic algorithm--constrained optimization

"... In PAGE 4: ... The confidence intervals for 95% confidence level were calculated for both the algorithms. Table2... ..."

### Table 2.2: Quadratically constrained optimization program for policy optimization by Amato et al. [2]

2006

Cited by 1

### Table 3.1: Hierarchy discovery and policy optimization framed as a quarticly-constrained optimization problem

2006

Cited by 1

### Table 2: Non-convex quarticly constrained optimization problem for hierarchy and policy discovery in bounded stochastic recursive controllers.

in Abstract

"... In PAGE 5: ... 3.3 Algorithms Since the problem in Table2 has non-convex (quartic) constraints in Eq. 5 and 6, it is difficult to solve.... In PAGE 5: ... 5 and 6, it is difficult to solve. We consider three approaches inspired from the techniques for non-hierarchical controllers: Non-convex optimization: Use a general non-linear solver, such as SNOPT, to directly tackle the optimization problem in Table2 . This is the most convenient approach, however a globally optimal solution may not be found due to the non-convex nature of the problem.... In PAGE 7: ... 4 Experiments We report on some preliminary experiments with three toy problems (paint, shuttle and maze) from the POMDP repository3. We used the SNOPT package to directly solve the non-convex optimization problem in Table2 and bounded hierarchical policy iteration (BHPI) to solve it iteratively. Table 3 reports the running time and the value of the hierarchical policies found.... ..."

### Table 2: Non-convex quarticly constrained optimization problem for hierarchy and policy discovery in bounded stochastic recursive controllers.

in Abstract

"... In PAGE 5: ... 3.3 Algorithms Since the problem in Table2 has non-convex (quartic) constraints in Eq. 5 and 6, it is difficult to solve.... In PAGE 5: ... 5 and 6, it is difficult to solve. We consider three approaches inspired from the techniques for non-hierarchical controllers: Non-convex optimization: Use a general non-linear solver, such as SNOPT, to directly tackle the optimization problem in Table2 . This is the most convenient approach, however a globally optimal solution may not be found due to the non-convex nature of the problem.... In PAGE 7: ... 4 Experiments We report on some preliminary experiments with three toy problems (paint, shuttle and maze) from the POMDP repository3. We used the SNOPT package to directly solve the non-convex optimization problem in Table2 and bounded hierarchical policy iteration (BHPI) to solve it iteratively. Table 3 reports the running time and the value of the hierarchical policies found.... ..."