### Table 2: Estimated and nal switching points of the state constrained time optimal motion.

### Table 2. Optimal Control Gains

"... In PAGE 11: ...The problem is written as a constraint minimization of the weighted goal function, so the lower the norm, the closer the controller approaches the goal. Table2 gathers the resulting optimal controller gains.Table 3 shows the resulting norm val- ues.... ..."

### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 1 Number of iterations to solve the optimal control problems. Optimal control Decoupled Coupled

1995

"... In PAGE 10: ....2. The number of linear systems needed is given in Table 1. While Table1 indicates that the decoupled approach is more e cient in terms of linear system solves, in applications with ill{conditioned Cy(x) the coupled ap- proach may be favorable. The reason is that in this case the decoupled approach may underestimate the size of Wk (sk)u vastly and, as a consequence, may require more... In PAGE 26: ...x = 20. The upper and lower bounds are bi = 0:01, ai = ?1000, i = 1; : : :; n ? m. We ran the exact and inexact TRIP SQP algorithms using decoupled and cou- pled approaches and reduced and full Hessians. The total number of iterations for each case is given in Table1 . The quantities f(x), kC(x)k, and kD(x)W(x)Trf(x)k are plotted in Figure 9.... In PAGE 28: ... The upper and lower bounds are bi = 5, ai = ?1000, i = 1; : : :; n ? m. The total number of iterations needed by the inexact TRIP SQP algorithms to solve this problem are presented in Table1 . In all situations but one, all the steps were accepted.... ..."

Cited by 14

### Table 1. Comparison of results for various approaches.

"... In PAGE 8: ... 4. Numerical Results Table1 compares the balance and uniformity (t,s) of (n,2) de Bruijn sequences... In PAGE 9: ... In the case of Algorithm II, the characteristics of the sequences obtained by the optimal mappings with respect to both balance and uniformity criteria are shown. ------------------------- Table1 goes here ------------------------- In Table 1, we observe that: 1. Although Algorithm I generates sequences with optimal uniformity (minimum s), the corresponding balance criterion t is rather large.... In PAGE 9: ... In the case of Algorithm II, the characteristics of the sequences obtained by the optimal mappings with respect to both balance and uniformity criteria are shown. -------------------------Table 1 goes here ------------------------- In Table1 , we observe that: 1. Although Algorithm I generates sequences with optimal uniformity (minimum s), the corresponding balance criterion t is rather large.... ..."

### Table 1: Performance Measures for Job-shop Scheduling and Control

2001

"... In PAGE 2: ... Our distributed, evolutionary approach to scheduling avoids these problems by removing the requirement for a truly optimal solution, requiring instead only a towards-optimal (but practical and useful) solution. The goal is to optimize (often) conflicting local and global performance measures (French, 1983), as outlined in columns one and two of Table1 . A secondary goal is to minimize the variance in the global stability measures in column three, in order to maximize the stability of the system.... ..."

Cited by 1

### TABLE 9.1 Number of iterations to solve the optimal control problems.

1995

Cited by 14

### TABLE 9.1 Number of iterations to solve the optimal control problems.

1995

Cited by 14

### Table II. Comparison of preconditioners for sparse optimal control problems.

### Table 6.8 Dimensions of Optimal Control problems. Problem m n Problem m n

1997

Cited by 146