### Table 2: Objective functions, constraints and optimization problems

2003

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### Table 1: Constraints to optimization problems by difierent sets J J Constraints

### Table 3.2: Constraints for the 29 variable HSCT optimization problem.

### Table 4. Problem dimension statistics. Problem Variables Constraints Optimal Value Markowitz 1200 201 -0.526165

2000

"... In PAGE 14: ...able 5. Total timing from each solver in seconds. Solver Markowitz Minimal Nonnegative Structural LANCELOT 503 106 3 mem MINOS sup sup sup inf NPSOL 538 657 191 mem PATH 84 333 2 res PATH (merit) 123 221 4 18,375 SNOPT itr sup sup ini Here a keyword in the table identi es that the solver has di culty solving this problem, where mem identi es that the solver could not allocate enough spaces, sup identi es that the solver reported the superbasics limit is too small, itr identi es that the solver reached its iteration limits, inf identi- es that the solver reported problem is unbounded, res identi es that the solver exceeded the resource limits and ini identi es that the solver found the problem is infeasible due to a bad starting point. Optimal solution val- ues from all successfully solved problems are the same for all solvers, and are reported in Table4 . Note that MINOS and SNOPT failed to solve each of these large problems, while PATHNLP with merit function solved all of them.... ..."

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### Table 2: Average constraint checks required to nd an optimal solution for various problems and walk prob- abilities.

1995

"... In PAGE 4: ...5. Table2 shows that e ects on number of constraint checks required to nd an optimal solution vary in the same way as run time. However, the overall rate of constraint checks tends to increase with problem di culty as measured by run time, from about 30 to 50 thousand constraint checks per second.... ..."

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### Table 1 Optimization Problem Statement

1999

"... In PAGE 14: ... The first formulation attempts to maximize fuel economy subject to performance constraints. The optimization problem statement is shown in Table1 . A second problem formulation was devised to minimize the 0 to 60 mph acceleration time while maintaining a relatively high fuel economy and satisfying other performance constraints.... ..."

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### Table 5: Set of benchmark problems used: application, number of constraints, number of variables and optimal solutions as reported in MIPLIB.

2004

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### Table 5: Set of benchmark problems used: application, number of constraints, number of variables and optimal solutions as reported in MIPLIB.

2004

Cited by 2

### Table 1: Summary of the sizes of the optimization problems for different norms. (See Appendix B for the definitions of the constraints in linear programming.)

2000

"... In PAGE 7: ... In contrast, in our framework the confidence C3B4DCBN AM C5DDB5 is com- pared to D1CPDCD6BI BPDD C3B4DCBN AM C5D6B5 and has only D1 slack variables in the primal program. In Table1 we summarize the properties of the program- s discussed above. As shown in the table, the advantage of using D0BE in the objective function is that the number of vari- ables in the dual problem in only a function of on CZ and D1 and does not depend on the number columns D0 in C5.... In PAGE 7: ... (24) can be solved using standard QP techniques. As shown in Table1 the dual program depends on D1CZ variables and has CZD1 B7 D1 con- straints all together. Converting the dual program in Eq.... ..."

Cited by 79

### Table 1: Summary of the sizes of the optimization problems for different norms. (See Appendix B for the definitions of the constraints in linear programming.)

2000

"... In PAGE 7: ... In contrast, in our framework the confidence C3B4DCBN AM C5DDB5 is com- pared to D1CPDCD6BI BPDD C3B4DCBN AM C5D6B5 and has only D1 slack variables in the primal program. In Table1 we summarize the properties of the programs discussed above. As shown in the table, the advantage of using D0BE in the objective function is that the number of vari- ables in the dual problem in only a function of on CZ and D1 and does not depend on the number columns D0 in C5.... In PAGE 7: ... (24) can be solved using standard QP techniques. As shown in Table1 the dual program depends on D1CZ variables and has CZD1 B7 D1 con- straints all together. Converting the dual program in Eq.... ..."

Cited by 79