### Table 4: Number of function evaluations and projections required by the optimization method for the di erent implementations of the CG iteration. n denotes the number of variables and m the number of general constraints (equalities or inequalities), excluding simple bounds.

"... In PAGE 25: ... We used the augmented system and normal equations approaches to compute projections, and for each of these strategies we tried the standard CG iteration (stand) and the residual update strategy (update) with iterative re nement described in Algorithm IV. The results are given in Table4 , where \fevals quot; denotes the total number of evaluations of the objective function of the nonlinear problem, and \projections quot; represents the total number of times that a projection operation was performed during the optimization. A *** indicates that the optimization algorithm was unable to locate the solution.... ..."

### Table 1: Numerical results of NOPTIQ and l-BFGS-B. The number of bounds on the variables is denoted by nb.

2003

"... In PAGE 12: ... In the same way, ti gt; 0 whenever NOPTIQ is better than the other code in term of CPU time. The numerical tests NOPTIQ versus l-BFGS-B are reported in Table1 (Appendix B) and Figure 1. These tests include only bound constraints problems, because l-BFGS-B cannot solve problems with general inequality constraints.... ..."

### Table 1: Finger/Phalangeal contribution for a cylin- drical grip. We have thus formulated the problem of computing hand feedback forces into that of solving a general op- timisation problem de ned by the minimisation crite- rion F2 (eq. 7) subject to constraints given by relations 3, 4, 5. The solution of such a constraint minimisa- tion problem can be obtained by using several meth- ods [12], like for instance the iterative, Kuhn-Tucker method. This is a generalisation of the Langrangian method for constraint minimisation problems contain- ing inequality constraints. For each such constraint,

1997

Cited by 1

### Table 1: The ranks of some example constraints

2003

"... In PAGE 22: ...2 Bounds on the rank We describe some general methods to obtain upper and lower bounds on the N-rank and N+-rank of valid inequalities, and extend them to the NFR-rank. We also illustrate the use of these methods on a few valid constraints for the stable set problem (see Table1 on page 27). The N-rank of an inequality valid for STAB(G) depends only on the subgraph induced by those vertices with a nonzero coefficient, and similarly for N+,NFR and NFR+.... ..."

Cited by 15

### Table 1: The ranks of some example constraints

2003

"... In PAGE 22: ...2 Bounds on the rank We describe some general methods to obtain upper and lower bounds on the N-rank and N+-rank of valid inequalities, and extend them to the NFR-rank. We also illustrate the use of these methods on a few valid constraints for the stable set problem (see Table1 on page 27). The N-rank of an inequality valid for STAB(G) depends only on the subgraph induced by those vertices with a nonzero coefficient, and similarly for N+,NFR and NFR+.... ..."

Cited by 15

### Table 6. Additional Primal Degenerate Bound Constraints

"... In PAGE 16: ...appears to be hardly affected. (An exception is the relative difficulty IP appears to have under primal degeneracy on bound constraints, Table6 , a case which requires further study.) More particularly, degeneracy on the inequality constraints makes little difference to the speed of convergence of projected gradient methods, so PDPG/N is not superior to PDPG in terms of number of iterations required.... In PAGE 19: ...90/198 9.21/21 Table6 . indicates that PDPG/N may be generally superior to PDPG and the interior-point method under primal degeneracy of bound constraints on the control variables.... ..."

### Table 3. Performance comparisons on ternary non-linear inequality constraints

2003

Cited by 12

### Table 5. Runtime results on QPs with both equality and inequality constraints.

2001

Cited by 3