Results of convex QP problems: performance profiles
The following performance
profiles are based on benchmark
result of Hans
Mittelmann. The profiles in this page are in log2 scale.
The first profile includes only general NLP solvers.
To put things into perspective, in the next profile we add two
commercial specialized QP solvers, CPLEX and XPRESS-MP. While the NLP
codes look at
the problem as at a general NLP (perhaps convex) problem, the two other
codes "know" they are solving a convex QP problem. The enormous
speed-up is mainly due to pre-processing.
The codes-versions:
LOQO-6.03
CPLEX-8.0 Barrier
Solver
XPRESS-MP-14.10
Barrier Solver
KNITRO-3.0
(iterative)
KNITRO-3.0
(direct)
PENNON-1.3
Problem statistics:
| no |
example |
var |
bounds |
equal |
nz(A) |
nz(Q) |
| 1 |
BOYD1 |
93261 |
93261 |
18 |
802156 |
93261 |
| 2 |
BOYD2 |
93263 |
93263 |
186531 |
423784 |
2 |
| 3 |
CONT-201 |
40397 |
40397 |
40198 |
199199 |
10400 |
| 4 |
CONT-300 |
90597 |
90597 |
90298 |
448799 |
23100 |
| 5 |
CVXQP1_L |
10000 |
10000 |
5000 |
14998 |
69968 |
| 6 |
CVXQP2_L |
10000 |
10000 |
2500 |
7499 |
69968 |
| 7 |
CVXQP3_L |
10000 |
10000 |
7500 |
22497 |
69968 |
| 8 |
EXDATA |
1500 |
1500 |
3001 |
7500 |
2250000 |
| 9 |
CONT5_400 |
160800 |
160800 |
160400 |
959203 |
801 |
| 10 |
CONT5_600 |
361200 |
361200 |
360600 |
2158803 |
1201 |
| 11 |
CONT5_800 |
641600 |
641600 |
640800 |
3838403 |
1601 |
| 12 |
TWOD_30 |
29584 |
29584 |
28710 |
259405 |
1831 |
| 13 |
TWOD_40 |
68644 |
68644 |
67080 |
621075 |
3241 |
| 14 |
TWOD_50 |
132304 |
132304 |
129850 |
1220345 |
5051 |
| 15 |
SQP2500-1 |
2500 |
0 |
2000 |
49821 |
1478602 |
| 16 |
SQP2500-2 |
2500 |
0 |
2000 |
49819 |
31190 |
| 17 |
SQP2500-3 |
2500 |
0 |
4500 |
112573 |
1478602 |
Michal
Kocvara
June 30, 2003