### Table 1. Primal-dual interior-point method: Summary of the algorithm.

"... In PAGE 20: ... Assume that yy gt; 0 and zy are distinct. Let fy i ; z i gi=1; be the sequence of iterates generated by the interior-point method as described in Table1 and de ne d = P i=1 y i z i . Assume that = n + 1 and that the sequence S = conv(z 1 ; : : : ; z ) is initialized by S0 and is converging.... ..."

Cited by 1

### Table 4: Statistics for problems with multiplicity 1. BT refers to the Bundle Trust method and IP refers to our Interior-Point method.

1996

"... In PAGE 21: ...rom (6.15) that (y; Z) is feasible for the dual. Finally, optimality follows from the absence of a duality gap: tr(ZX) = trf( maxI ? C)AATg = 0 The last equality follows from the fact that the columns of A are eigenvectors of C asso- ciated with the maximal eigenvalue. Table4 shows the comparison between the bundle trust method, see [26], and our interior-point method when the optimal eigenvalue is a singleton (k = 1). For these problems, the bundle trust method is three to four times faster (computing times are given for a Silicon Graphics Indigo workstation R 4000).... ..."

Cited by 184

### Table 1: Rough comparison among the standard primal-dual interior-point method, conver- sion method and completion method.

2003

"... In PAGE 15: ... We assume that each data matrix Ap has only O(1) nonzero elements (p = 0; 1; : : : ; m). In Table1 , \other parts quot; includes the computations of dY 2 Sn(E; 0), dX 2 Sn(F; ?), the primal and dual step lengths, etc. Table 1: Rough comparison among the standard primal-dual interior-point method, conver- sion method and completion method.... ..."

Cited by 16

### Table 3: The number of PCG iterations during the interior point method iterations.

2007

"... In PAGE 20: ... For one problem, chr22b, using the mixed approach leads to significantly fewer IPM iterations being required. In order to give an insight into the behaviour of the preconditioned conjugate gradients, in Table3 we report the number of PCG iterations needed to solve a particular linear system. First, we report separately this number for the last interior point iteration when our preconditioner is supposed to behave best.... ..."

### Table 3: The number of PCG iterations during the interior point method iterations.

2006

"... In PAGE 20: ... For one problem, chr22b, using the mixed approach leads to signi cantly fewer IPM iterations being required. In order to give an insight into the behaviour of the preconditioned conjugate gradients, in Table3 we report the number of PCG iterations needed to solve a particular linear system. First, we report separately this number for the last interior point iteration when our preconditioner is supposed to behave best.... ..."

### Table 3: Statistics for problems with multiplicity 1. BT refers to the Bundle Trust method and IP refers to our Interior-Point method.

1994

"... In PAGE 23: ...rom (6.15) that (y; Z) is feasible for the dual. Finally, optimality follows from the absence of a duality gap: tr(ZX) = trf( maxI ? C)AATg = 0 The last equality follows from the fact that the columns of A are eigenvectors of C asso- ciated with the maximal eigenvalue. Table3 shows the comparison between the bundle trust method and our interior-point method when the optimal eigenvalue is a singleton (k = 1). For these problems, the bundle trust method is three to four times faster.... ..."

### Table 2: Statistics for problems with multiplicity 1. BT refers to the Bundle Trust method and IP refers to our Interior-Point method.

"... In PAGE 13: ...rimal and it is clear from (5.2) that (y; Z) is feasible for the dual. Finally, optimality follows from the absense of a duality gap: tr(ZX) = trf(C ? minI)AATg = 0 The last equality follows from the fact that the columns of A are eigenvectors of C associated with the minimal eigenvalue. Table2 shows the comparison between the bundle trust method and our interior-point method when the optimal eigenvalue is a singleton (k = 1). For these problems, the bundle trust method is three to four times faster.... ..."

### TABLE 3. SAT: Comparison of Simplex and interior point methods

1998

Cited by 13

### Table 3: SAT: Comparison of Simplex and interior point methods

"... In PAGE 9: ... Instances with up to 1000 variables and 32,000 clauses were solved. Compared with the Simplex Method approach on small problems #28 Table3 #29, speedups of over two orders of magnitude were observed. Furthermore, the in- terior point approachwas successful in proving satis#0Cabilityinover 250 instances that the Simplex Method approach failed.... ..."