### Table 3: Reduction in Optimality Gap by the Disjunctive Cuts for the LP Relaxations.

2006

"... In PAGE 26: ... Here we calculate the relative optimality gap as follows: Relative optimality gap (Gap) = cTzLP cTz t cTz t : Number of Scenarios (N) 82 Number of Stocks (n) 300 Number of binary variables 6724 Number of continuous variables 300 Number of linear constraints 6807 Table 4: Dimensions of the Problem. Table3 demonstrates the e ectiveness of the disjunctive cuts in strengthening the LP relaxations of problem (4) and reducing the optimality gap. Figure 6 illustrates that the disjunctive cuts accelerate the convergence to a better relative op- timality gap, in addition to improving the lower and upper bounds on optimal objective function value.... ..."

### Table 2: Reduction in Optimality Gap by the Disjunctive Cuts for CPLEX. ( ; : Only 30 and 50 disjunctive cuts are added, respectively.)

2006

"... In PAGE 25: ... In this way, we generated 100 disjunctive cuts and added them to the formulation of MBLP. Table2 shows the relative optimality gap values obtained with and without the disjunctive cuts and also the reduction in relative optimality gap by the use of such cuts. Adding the disjunctive cuts to the formulation of MBLP tightens the feasible region, which results in reducing the optimality gap, as seen in Table 2.... In PAGE 25: ... Table 2 shows the relative optimality gap values obtained with and without the disjunctive cuts and also the reduction in relative optimality gap by the use of such cuts. Adding the disjunctive cuts to the formulation of MBLP tightens the feasible region, which results in reducing the optimality gap, as seen in Table2 . The reduction in optimality gap is due to generally improving both the upper bound and lower bound on the optimal objective function value.... ..."

### 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 7. Constraint Disjunction Associated With the Functional Relationships

"... In PAGE 11: ...able 6. Test Data Summary for Experiment 3 (Cruise Control).............................................................. 30 Table7 .... In PAGE 64: ....2.6 FUNCTIONAL REQUIREMENTS The functional requirements define the set of functional relationships for each element of the output (vt_data) and the associated constraints. Table7 summarizes the functional relationships and the constraint disjunction under which the functional relationship is required to be valid. The top part of the table identifies the constraint, and the bottom part of the table identifies the functional relationship.... ..."

### Table 1. Evaluating negative disjunctive queries.

### Table 8 Mission constraints for optimization runs.

2004

"... In PAGE 12: ... These inputs and bounds are sum- marized in Table 7. The design constraints presented in Table8 were also imposed. Minimum Boom Loudness (dBA) Optimization The minimum boom optimization used the response surface fit value for sonic boom strength (measured as dBA with finite rise time) as the objective.... ..."

### Table 3: Bounds required in Equation 3 for a disjunction

### Table 3: Bounds required in Equation 3 for a disjunction

### Table 1: How all constraints for the disjunctions on all fractional variables are partitioned among tight and non-tight constraints.

1998

"... In PAGE 9: ... This measure will be defined as follows: (M6) M6 qBNi BP 1 iff constraint i in term q has a negative reduced cost in the intersection cut basis. In Table1 we present observations about the number of tight constraints contributing to the lower term B4dx AK 0B5, the upper term B4dx AL 1B5 or does not contribute in the intersection cut (by contributing we mean having a non-zero multiplier, in this case in the (CLP2) basis having the intersection cut as its solution). For the non-tight constraints we count how many constraints are violated at a lower point x1BNj but not an upper, at an upper point x2BNj but not a lower, violated at both, or is not violated at all.... ..."

### Table 2 Summary of handling of constraints in various global optimization algorithms.

"... In PAGE 10: ... However, ex- tensive numerical results using these techniques have not been published. (See Table2 ; blank spaces mean the feature is absent.) Handling of simple bound constraints through the tessellation process has been... ..."