Abstract
The implementation of a linear programming interior point solver is described that is based on iterative linear algebra. The linear systems are preconditioned by a basis matrix, which is updated from one interior point iteration to the next to bound the entries in a certain tableau matrix. The update scheme is based on simplex-type pivot operations and is implemented using linear algebra techniques from the revised simplex method. An initial basis is constructed by a crash procedure after a few interior point iterations. The basis at the end of the interior point solve provides the starting basis for a crossover method which recovers a basic solution to the linear program. Results of a computational study on a diverse set of medium to large-scale problems are discussed.
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Notes
For a matrix A the expression \(|A|\) is meant componentwise.
References
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Appendix A: Test set and solution times
Appendix A: Test set and solution times
The LP models have been obtained from the following sources:
-
(1)
J. Castro: http://www-eio.upc.es/~jcastro/
-
(a)
huge CTA instances
-
(b)
integrated refinery problems
-
(c)
L1.zip
-
(d)
Linf.zip
-
(a)
-
(2)
J. A. J. Hall: http://www.maths.ed.ac.uk/hall/PublicLP/
-
(3)
Kennington collection: http://www.netlib.org/lp/data/kennington/index.html
-
(4)
C. Mészáros: http://old.sztaki.hu/~meszaros/public_ftp/lptestset/
-
(a)
misc
-
(b)
New
-
(c)
problematic
-
(d)
stochlp
-
(a)
-
(5)
MIPLIB 2010: http://miplib.zib.de/download/miplib2010-complete.tgz
-
(6)
H. Mittelmann: http://plato.asu.edu/ftp/lptestset/
-
(a)
fome
-
(b)
misc
-
(c)
nug
-
(d)
pds
-
(e)
rail
-
(a)
-
(7)
Netlib collection: http://www.netlib.org/lp/data/index.html
For mixed-integer problems, the canonical LP relaxation was used.
In the following table, the columns headed “\({\bar{m}}\)”, “\({\bar{n}}\)” and “\({{\,\mathrm{nnz}\,}}\)” provide the number of rows, columns and nonzero entries of the constraint matrix \({\bar{A}}\) in the problem formulation (2a), after the LP model was preprocessed by the Gurobi LP presolve. The column block headed “IPX” provides the runtime of the IPX interior point solver (“IPM”), of the IPX crossover push phases (“push”) and of the clean-up using the Gurobi simplex (“simplex”); the latter field is empty if no clean-up was needed. The column headed “total” gives the sum of the three runtimes. The column block headed “Gurobi” provides the runtimes of the Gurobi interior point solver (“IPM”) and crossover (“crossover”) as well as their sum (“total”). The presolve time has been excluded from these figures. Computation times are in seconds and were obtained on an Intel i5-6500 CPU (4 cores, 3.2 GHz, 6 MB L3 cache) and 8 GB of physical memory. Logfiles from IPX and Gurobi, from which the runtimes were extracted, are available at https://github.com/ERGO-Code/ipx/tree/master/benchmark.
src | Name | \({\bar{m}}\) | \({\bar{n}}\) | \({{\,\mathrm{nnz}\,}}\) | IPX | Gurobi | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
Total | IPM | Push | Cleanup | Total | IPM | Crossover | |||||
1a | L1_sixm250obs | 154,168 | 308,284 | 639,901 | 180.1 | 176.5 | 3.6 | 43.5 | 42.1 | 1.4 | |
1a | L1_sixm500obs | 283,055 | 565,680 | 1,196,860 | 553.8 | 506.0 | 47.8 | 471.8 | 468.7 | 3.1 | |
1b | srd120 | 186,440 | 357,070 | 9,804,510 | 329.5 | 327.4 | 2.1 | 496.5 | 484.9 | 11.6 | |
1b | srd240 | 372,920 | 714,190 | 36,457,110 | 1883.3 | 1877.2 | 6.1 | 3615.5 | 3577.2 | 38.3 | |
1c | L1_bts4 | 25,611 | 69,900 | 181,413 | 5.7 | 5.6 | 0.1 | 1.4 | 1.3 | 0.2 | |
1c | L1_five20b | 28,342 | 62,986 | 187,981 | 47.4 | 47.2 | 0.1 | 6.5 | 3.7 | 2.8 | |
1d | Linf_bts4 | 61,465 | 70,128 | 287,954 | 11.1 | 10.8r | 0.3 | 0.1 | 49.3 | 48.7 | 0.6 |
1d | Linf_five20b | 60,911 | 63,458 | 285,418 | 243.5 | 64.6r | 16.3 | 162.6 | 25.1 | 10.8 | 14.3 |
2 | dcp2 | 13,927 | 25,376 | 281,550 | 5.7 | 5.7r | 0.0 | 0.7 | 0.6 | 0.2 | |
3 | cre-b | 5213 | 31,720 | 107,039 | 2.3 | 2.3 | 0.0 | 0.4 | 0.4 | 0.0 | |
3 | ken-18 | 39,855 | 89,346 | 204,936 | 5.5 | 5.5 | 0.1 | 1.3 | 1.1 | 0.2 | |
3 | osa-60 | 10,209 | 224,125 | 584,253 | 5.7 | 5.6 | 0.1 | 1.1 | 1.0 | 0.1 | |
4a | bas1lp | 5409 | 4443 | 582,390 | 4.0 | 3.8 | 0.2 | 1.2 | 1.0 | 0.1 | |
4a | baxter | 18,867 | 10,742 | 78,412 | 2.5 | 2.4 | 0.1 | 1.9 | 1.9 | 0.1 | |
4a | co9 | 6784 | 10,675 | 81,809 | 2.1 | 2.1 | 0.0 | 0.4 | 0.4 | 0.1 | |
4a | dbic1 | 33,598 | 140,205 | 781,668 | 58.4 | 46.7 | 11.7 | 12.0 | 2.8 | 9.2 | |
4a | dbir1 | 7150 | 24,862 | 994,828 | 17.3 | 16.3 | 1.0 | 1.6 | 1.4 | 0.2 | |
4a | e18 | 24,598 | 14,211 | 131,991 | 12.6 | 12.3 | 0.2 | 63.2 | 63.1 | 0.2 | |
4a | ex3sta1 | 12,602 | 12,675 | 54,377 | 3.5 | 3.4 | 0.0 | 0.4 | 0.2 | 0.2 | |
4a | jendrec1 | 2109 | 3535 | 88,915 | 0.9 | 0.9 | 0.0 | 1.1 | 0.7r | 0.4 | |
4a | lpl1 | 32,427 | 82,733 | 252,587 | 21.9 | 21.4 | 0.5 | 4.1 | 1.8 | 2.3 | |
4a | mod2 | 23,706 | 24,005 | 114,068 | 6.1 | 6.1 | 0.0 | 1.5 | 1.2 | 0.2 | |
4a | model10 | 2961 | 10,373 | 94,372 | 1.6 | 1.5 | 0.0 | 0.0 | 0.3 | 0.2 | 0.1 |
4a | nemsemm1 | 2829 | 36,052 | 495,916 | 5.8 | 5.8 | 0.0 | 0.6 | 0.6 | 0.1 | |
4a | nl | 5290 | 7997 | 36,524 | 1.0 | 1.0 | 0.0 | 0.4 | 0.4 | 0.0 | |
4a | nsct1 | 7696 | 11,297 | 589,578 | 7.7 | 7.5 | 0.2 | 3.5 | 3.4 | 0.1 | |
4a | p010 | 8907 | 17,770 | 60,150 | 4.3 | 4.2 | 0.0 | 0.1 | 0.1 | 0.0 | |
4a | rat7a | 2152 | 6772 | 156,249 | 2.0 | 2.0 | 0.0 | 0.5 | 0.3 | 0.2 | |
4a | route | 20,779 | 23,923 | 184,576 | 2.4 | 2.3 | 0.1 | 0.4 | 0.4 | 0.0 | |
4a | stat96v1 | 4624 | 187,892 | 562,110 | 21.7 | 21.2r | 0.4 | 0.1 | 20.8 | 4.9r | 15.8 |
4a | stat96v3 | 26,274 | 1,090,091 | 3,250,147 | 1423.9 | 470.1r | 14.0 | 939.9 | 8063.5 | 5.2r | 8058.3 |
4a | ulevimin | 4594 | 41,225 | 135,479 | 3.9 | 3.9 | 0.0 | 0.6 | 0.5 | 0.1 | |
4a | world | 23,640 | 25,839 | 114,431 | 6.7 | 6.7 | 0.0 | 1.7 | 1.3 | 0.4 | |
4b | degme | 185,501 | 659,415 | 8,127,528 | 2496.8 | 2495.9 | 0.9 | 166.4 | 79.8 | 86.6 | |
4b | karted | 46,501 | 133,114 | 1,770,336 | 499.6 | 499.4 | 0.2 | 144.9 | 27.2 | 117.7 | |
4b | tp-6 | 142,752 | 1,014,301 | 11,537,419 | 2820.9 | 2820.0 | 0.8 | 66.0 | 42.0 | 24.0 | |
4b | ts-palko | 22,002 | 47,235 | 1,076,903 | 314.7 | 314.5 | 0.2 | 79.2 | 8.6 | 70.6 | |
4c | gen4 | 1475 | 4173 | 104,236 | 12.3 | 11.8r | 0.5 | 1.8 | 0.5 | 1.3 | |
4c | l30 | 2698 | 15,360 | 51,093 | 1.8 | 1.6 | 0.1 | 0.1 | 4.0 | 0.8 | 3.2 |
4d | fxm3_16 | 32,946 | 57,391 | 315,606 | 7.2 | 7.2 | 0.1 | 1.0 | 0.8 | 0.2 | |
4d | pltexpa4_6 | 13,693 | 24,221 | 70,946 | 3.0 | 3.0 | 0.1 | 1.3 | 1.2 | 0.1 | |
4d | scfxm1-2r-256 | 25,922 | 45,663 | 158,006 | 8.1 | 8.1 | 0.1 | 1.6 | 1.0 | 0.5 | |
4d | stormg2-125 | 47,536 | 129,869 | 358,498 | 28.3 | 28.1 | 0.2 | 2.8 | 2.5 | 0.4 | |
4d | stormg2_1000 | 380,036 | 1,038,119 | 2,865,373 | f | 29.3 | 24.1 | 5.2 | |||
5 | 30_70_45_095_100 | 12,515 | 10,967 | 46,614 | 2.4 | 1.0 | 1.5 | 1.2 | 0.3 | 0.9 | |
5 | app1-2 | 52,261 | 26,265 | 194,705 | 4.5 | 4.4 | 0.1 | 1.0 | 0.9 | 0.2 | |
5 | atlanta-ip | 19,835 | 17,484 | 182,879 | 10.2 | 10.0 | 0.2 | 4.8 | 4.5 | 0.3 | |
5 | bab3 | 22,478 | 393,457 | 3,097,799 | 120.1 | 119.8 | 0.3 | 6.2 | 5.9 | 0.3 | |
5 | bley_xl1 | 175,178 | 5724 | 867,393 | 10.4 | 7.8 | 2.6 | 13.5 | 13.2 | 0.3 | |
5 | buildingenergy | 225,031 | 128,695 | 683,844 | 262.5 | 260.5 | 2.0 | 6.1 | 5.7 | 0.5 | |
5 | circ10-3 | 42,620 | 2700 | 307,320 | 1.2 | 1.0 | 0.3 | 0.6 | 0.4 | 0.2 | |
5 | core4872-1529 | 4607 | 24,098 | 184,762 | 4.2 | 4.1 | 0.1 | 1.6 | 1.3 | 0.3 | |
5 | dano3mip | 3150 | 13,837 | 79,530 | 1.7 | 1.7 | 0.0 | 1.1 | 0.9 | 0.2 | |
5 | datt256 | 9863 | 196,147 | 1,124,622 | 1218.3 | 158.1 | 1060.2 | 718.3 | 1.0 | 717.3 | |
5 | dc1l | 1650 | 35,496 | 424,338 | 5.9 | 5.9 | 0.1 | 1.1 | 1.0 | 0.1 | |
5 | dolom1 | 1802 | 10,825 | 176,976 | 2.4 | 2.4 | 0.0 | 0.6 | 0.5 | 0.0 | |
5 | ds-big | 1042 | 173,029 | 4,573,582 | 196.9 | 195.4 | 1.6 | 6.0 | 5.0 | 1.0 | |
5 | ex10 | 62,932 | 15,896 | 1,031,940 | 38.7 | 12.9 | 25.8 | 121.8 | 114.4 | 7.4 | |
5 | f2000 | 10,495 | 3995 | 29,490 | 3.6 | 2.3 | 1.3 | 2.8 | 0.9 | 1.9 | |
5 | germanrr | 5524 | 10,650 | 159,548 | 2.0 | 1.9 | 0.0 | 0.0 | 0.3 | 0.3 | 0.0 |
5 | gmut-75-50 | 2499 | 35,915 | 569,806 | 6.0 | 5.9 | 0.0 | 0.0 | 0.8 | 0.7 | 0.1 |
5 | in | 1,495,549 | 1,439,571 | 6,696,217 | 5381.1 | 4622.9 | 758.2 | 101.2 | 82.7 | 18.4 | |
5 | ivu06-big | 1177 | 2,197,774 | 22,556,378 | 2067.8 | 2064.9 | 2.9 | 34.3 | 30.7 | 3.6 | |
5 | ivu52 | 2116 | 157,543 | 2,178,871 | 69.2 | 68.4 | 0.8 | 3.5 | 3.2 | 0.3 | |
5 | map06 | 37,504 | 18,973 | 81,653 | 11.3 | 11.2 | 0.1 | 3.5 | 3.2 | 0.3 | |
5 | mining | 661,094 | 348,958 | 2,754,430 | 772.0 | 770.0 | 2.0 | 46.6 | 36.8 | 9.8 | |
5 | momentum3 | 56,421 | 13,334 | 566,199 | 25.7 | 25.6 | 0.2 | 22.1 | 18.0 | 4.0 | |
5 | msc98-ip | 15,293 | 12,823 | 81,666 | 4.1 | 3.6 | 0.3 | 0.2 | 3.0 | 2.6 | 0.4 |
5 | mspp16 | 524,814 | 4081 | 27,555,511 | 65.3 | 65.0 | 0.3 | 57.4 | 52.7 | 4.7 | |
5 | mzzv11 | 9316 | 9902 | 133,424 | 2.3 | 2.1 | 0.2 | 1.6 | 1.5r | 0.1 | |
5 | n15-3 | 28,860 | 153,140 | 575,246 | 19.0 | 18.6 | 0.3 | 2.4 | 2.1 | 0.3 | |
5 | n3seq24 | 5950 | 119,856 | 2,404,844 | 27.0 | 26.5 | 0.5 | 4.1 | 3.7 | 0.3 | |
5 | nb10tb | 94,742 | 49,744 | 802,185 | 92.8 | 78.2 | 0.6 | 14.0 | 53.6 | 41.9 | 11.7 |
5 | neos-1140050 | 3795 | 39,075 | 806,835 | 6.8 | 6.8 | 0.0 | 3.9 | 3.3 | 0.6 | |
5 | neos-1429212 | 29,416 | 64,404 | 1,222,493 | 34.1 | 31.4 | 2.6 | 3.3 | 1.9 | 1.4 | |
5 | neos-1605075 | 3464 | 4085 | 91,314 | 1.3 | 0.9 | 0.3 | 1.0 | 0.9 | 0.2 | |
5 | neos-476283 | 4312 | 6528 | 3,924,503 | 23.8 | 23.3 | 0.5 | 20.0 | 19.8 | 0.3 | |
5 | neos-506428 | 129,925 | 42,981 | 343,466 | 7.5 | 4.4 | 3.1 | 1.3 | 1.0 | 0.3 | |
5 | neos-520729 | 17,391 | 64,464 | 175,131 | 12.1 | 11.8 | 0.3 | 0.4 | 0.4 | 0.1 | |
5 | neos-631710 | 169,576 | 167,056 | 834,166 | 220.2 | 3.4 | 216.8 | 8.7 | 1.2 | 7.5 | |
5 | neos-738098 | 25,736 | 8981 | 100,842 | 2.6 | 1.5 | 1.1 | 0.6 | 0.5 | 0.1 | |
5 | neos-799711 | 12,660 | 11,615 | 40,152 | 1.4 | 1.3 | 0.1 | 0.5 | 0.4 | 0.1 | |
5 | neos-824661 | 18,804 | 29,920 | 122,230 | 2.0 | 1.7 | 0.3 | 0.3 | 0.2 | 0.1 | |
5 | neos-826694 | 6730 | 15,210 | 52,020 | 1.2 | 0.8 | 0.3 | 0.2 | 0.1 | 0.1 | |
5 | neos-933638 | 9642 | 8887 | 54,484 | 1.9 | 1.0 | 0.9 | 0.6 | 0.4 | 0.3 | |
5 | neos-941313 | 13,099 | 116,670 | 386,400 | 8.4 | 6.9 | 1.6 | 1.1 | 0.4 | 0.7 | |
5 | neos-948126 | 7208 | 7777 | 37,891 | 1.6 | 1.1 | 0.5 | 0.4 | 0.2 | 0.2 | |
5 | neos-957389 | 5114 | 6034 | 355,369 | 4.4 | 4.3 | 0.1 | 0.6 | 0.5 | 0.1 | |
5 | neos-984165 | 6921 | 7315 | 36,573 | 1.7 | 1.2 | 0.5 | 0.4 | 0.2 | 0.2 | |
5 | neos6 | 1036 | 8563 | 251,723 | 1.1 | 1.1 | 0.0 | 0.5 | 0.4 | 0.0 | |
5 | neos808444 | 17,729 | 19,330 | 119,357 | 2.8 | 1.2 | 1.6 | 0.6 | 0.4 | 0.3 |
5 | net12 | 13,975 | 14,115 | 80,108 | 2.8 | 2.8 | 0.0 | 4.4 | 4.4 | 0.0 | |
5 | netdiversion | 99,581 | 128,968 | 495,878 | 110.3 | 105.2 | 5.1 | 14.4 | 4.2 | 10.3 | |
5 | npmv07 | 60,835 | 162,180 | 378,798 | 23.1 | 22.9 | 0.2 | 3.7 | 3.5 | 0.2 | |
5 | ns1111636 | 13,453 | 76,462 | 283,284 | 5.3 | 5.1 | 0.2 | 0.5 | 0.4 | 0.1 | |
5 | ns1116954 | 131,865 | 11,928 | 409,850 | 7.0 | 2.1 | 4.9 | 12.2 | 11.7 | 0.4 | |
5 | ns1631475 | 24,074 | 22,485 | 100,023 | 4.6 | 4.4 | 0.3 | 1.0 | 0.5 | 0.5 | |
5 | ns1644855 | 30,597 | 30,199 | 2,100,495 | 49.5 | 47.9 | 1.6 | 131.6 | 131.2 | 0.5 | |
5 | ns1663818 | 167,047 | 123,027 | 20,177,986 | 1105.0 | 1077.8r | 27.3 | 208.3 | 197.3r | 10.9 | |
5 | ns1685374 | 43,195 | 9174 | 206,101 | 9.9 | 9.9 | 0.0 | 11.9 | 1.6 | 10.4 | |
5 | ns1696083 | 10,513 | 7748 | 371,757 | 4.9 | 4.9 | 0.1 | 1.7 | 1.6 | 0.1 | |
5 | ns1758913 | 615,190 | 17,824 | 1,265,492 | 26.2 | 19.6 | 6.6 | 21.0 | 3.9 | 17.1 | |
5 | ns1853823 | 223,144 | 213,176 | 1,346,924 | 492.6 | 473.3 | 19.3 | 32.7 | 20.8r | 11.9 | |
5 | ns1854840 | 143,236 | 135,754 | 844,834 | 136.5 | 124.1 | 12.4 | 6.2 | 4.7 | 1.6 | |
5 | ns1904248 | 146,398 | 38,262 | 371,070 | 6.6 | 1.7 | 4.9 | 0.8 | 0.7 | 0.2 | |
5 | ns1905797 | 51,876 | 18,188 | 239,156 | 1.6 | 1.5 | 0.1 | 11.4 | 11.3 | 0.1 | |
5 | ns2017839 | 49,884 | 53,364 | 298,482 | 20.2 | 20.1 | 0.1 | 0.0 | 7.3 | 3.2r | 4.1 |
5 | ns2118727 | 160,408 | 164,350 | 636,614 | 42.0 | 41.9 | 0.1 | 13.8 | 13.5 | 0.3 | |
5 | ns2122603 | 19,036 | 16,556 | 64,357 | f | 4.4 | 1.6 | 2.9 | |||
5 | ns2124243 | 32,277 | 48,893 | 192,513 | 4.8 | 4.4 | 0.4 | 0.6 | 0.3 | 0.3 | |
5 | ns2137859 | 99,385 | 99,462 | 593,332 | 11.6 | 11.4 | 0.2 | 2.7 | 2.1 | 0.5 | |
5 | ns894244 | 9479 | 16,399 | 68,362 | 3.1 | 2.6 | 0.5 | 0.8 | 0.6 | 0.2 | |
5 | ns930473 | 22,846 | 33,136 | 139,974 | 7.2 | 6.8 | 0.4 | 1.1 | 0.8 | 0.4 | |
5 | nsr8k | 6283 | 38,264 | 370,206 | 16.8 | 16.4 | 0.4 | 4.7 | 3.9 | 0.7 | |
5 | ofi | 105,107 | 222,217 | 848,037 | 135.5 | 134.7 | 0.8 | 0.1 | 29.0 | 28.5 | 0.5 |
5 | opm2-z11-s8 | 205,936 | 7653 | 473,063 | 19.4 | 10.9 | 8.6 | 22.4 | 15.0 | 7.4 | |
5 | opm2-z12-s7 | 297,892 | 10,336 | 678,441 | 44.4 | 20.4 | 23.9 | 37.8 | 23.2 | 14.6 | |
5 | pb-simp-nonunif | 123,532 | 11,798 | 298,082 | 1.3 | 1.0 | 0.3 | 1.3 | 0.7 | 0.5 | |
5 | rail02 | 54,524 | 192,618 | 599,436 | 71.0 | 62.3 | 8.6 | 45.2 | 42.0 | 3.2 | |
5 | rail03 | 129,647 | 567,095 | 1,349,518 | 399.2 | 318.7 | 80.5 | 55.4 | 48.7 | 6.8 |
5 | ramos3 | 2187 | 2187 | 32,805 | 4.6 | 1.0 | 3.6 | 4.4 | 0.3 | 4.1 | |
5 | reblock420 | 62,800 | 4200 | 138,670 | 1.9 | 1.2 | 0.8 | 0.8 | 0.6 | 0.3 | |
5 | rmatr100-p5 | 8685 | 8784 | 26,152 | 3.9 | 3.8 | 0.0 | 9.1 | 9.1 | 0.0 | |
5 | rmatr200-p5 | 37,617 | 37,816 | 113,048 | 56.5 | 55.7 | 0.8 | 1.3 | 1.2 | 0.1 | |
5 | rmine14 | 268,474 | 32,144 | 659,980 | 83.0 | 80.4 | 2.6 | 48.6 | 20.8 | 27.8 | |
5 | rmine21 | 1,441,506 | 162,402 | 3,514,014 | 2707.8 | 2580.2 | 127.7 | 1620.0 | 694.8 | 925.2 | |
5 | rocII-9-11 | 42,412 | 20,557 | 503,343 | 6.6 | 6.3 | 0.3 | 1.1 | 0.7 | 0.3 | |
5 | satellites3-40-fs | 28,171 | 54,578 | 199,798 | 22.0 | 14.7 | 7.4 | 6.2 | 3.1 | 3.1 | |
5 | satellites3-40 | 37,422 | 54,578 | 588,630 | 34.4 | 25.4 | 9.0 | 61.2 | 56.6 | 4.6 | |
5 | sct1 | 9171 | 14,514 | 85,676 | 4.2 | 4.1 | 0.1 | 1.3 | 1.2 | 0.1 | |
5 | shs1023 | 126,657 | 432,068 | 1,013,029 | 173.5 | 170.8 | 2.7 | 14.4 | 12.8 | 1.6 | |
5 | siena1 | 2211 | 13,482 | 254,310 | 3.9 | 3.8 | 0.1 | 1.1 | 1.0 | 0.1 | |
5 | sing161 | 150,806 | 464,036 | 1,459,828 | 281.9 | 273.6 | 8.3 | 13.6 | 12.1 | 1.5 | |
5 | sing359 | 153,253 | 428,748 | 1,408,257 | 268.7 | 258.4 | 10.3 | 11.9 | 10.1 | 1.8 | |
5 | sp97ar | 1692 | 14,100 | 281,317 | 1.4 | 1.4 | 0.0 | 0.2 | 0.2 | 0.0 | |
5 | splan1 | 521,819 | 1,253,087 | 5,088,694 | 5242.2 | 4989.8 | 250.4 | 1.9 | 1775.7 | 1587.6 | 188.1 |
5 | stockholm | 36,517 | 16,622 | 111,003 | 5.6 | 5.5 | 0.1 | 0.7 | 0.6 | 0.1 | |
5 | stp3d | 97,936 | 137,646 | 500,753 | 196.5 | 163.4 | 33.1 | 11.2 | 9.4 | 1.8 | |
5 | tanglegram1 | 68,210 | 34,501 | 204,158 | 7.3 | 5.8 | 1.5 | 7.7 | 0.3 | 7.4 | |
5 | triptim3 | 14,121 | 22,982 | 494,503 | 14.2 | 13.3 | 0.9 | 5.3 | 4.8 | 0.5 | |
5 | uc-case3 | 34,288 | 27,194 | 230,068 | 7.2 | 7.0 | 0.2 | 1.1 | 0.9 | 0.2 | |
5 | unitcal_7 | 43,301 | 25,767 | 109,859 | 12.5 | 12.1 | 0.4 | 1.1 | 0.9 | 0.2 | |
5 | van | 22,016 | 7360 | 481,408 | 2.7 | 2.7 | 0.0 | 7.5 | 7.3 | 0.1 | |
5 | vpphard | 39,140 | 43,395 | 332,904 | 8.2 | 7.2 | 1.0 | 3.7 | 3.4 | 0.3 | |
5 | vpphard2 | 136,399 | 139,234 | 561,958 | 26.2 | 25.8 | 0.4 | 36.6 | 36.3 | 0.3 | |
5 | wnq-n100-mw99-14 | 656,900 | 10,000 | 1,333,400 | 20.3 | 20.0 | 0.2 | 39.4 | 39.0 | 0.3 | |
6a | fome13 | 34,600 | 76,249 | 246,895 | 40.5 | 36.0 | 4.5 | 5.8 | 4.6 | 1.2 | |
6a | fome21 | 24,173 | 162,336 | 356,706 | 15.5 | 15.0 | 0.5 | 3.5 | 3.1 | 0.4 | |
6b | cont1 | 120,395 | 40,398 | 359,593 | 88.5 | 88.4 | 0.1 | 18.8 | 2.0 | 16.8 |
6b | cont11 | 120,395 | 80,396 | 359,593 | 668.6 | 641.7 | 4.8 | 22.1 | 250.0 | 1.9 | 248.1 |
6b | cont11_l | 1,468,599 | 981,396 | 4,403,001 | f | 3256.3 | 32.1 | 3224.2 | |||
6b | cont1_l | 1,918,399 | 641,598 | 5,752,001 | f | 1951.3 | 50.3 | 1900.9 | |||
6b | neos | 419,478 | 41,140 | 911,651 | 118.8 | 118.6 | 0.2 | 8.1 | 7.8 | 0.3 | |
6b | neos1 | 131,581 | 1892 | 468,009 | 7.9 | 7.8 | 0.1 | 1.4 | 1.3 | 0.1 | |
6b | neos3 | 512,209 | 6624 | 1,542,816 | 60.9 | 27.4 | 33.5 | 38.6 | 11.4 | 27.2 | |
6b | ns1687037 | 36,080 | 30,955 | 1,377,655 | 145.8 | 145.8 | 0.1 | 24.5 | 15.4 | 9.1 | |
6b | ns1688926 | 24,576 | 16,489 | 901,120 | f | 28.9 | 22.5r | 6.4 | |||
6b | sgpf5y6 | 19,499 | 39,020 | 109,247 | 3.4 | 3.3 | 0.1 | 1.7 | 1.4 | 0.3 | |
6b | watson_1 | 107,522 | 216,565 | 658,933 | 85.7 | 85.2 | 0.5 | 4.5 | 3.3 | 1.3 | |
6b | watson_2 | 185,474 | 378,986 | 1,040,238 | 193.8 | 192.7 | 1.1 | 6.5 | 3.5 | 3.0 | |
6c | nug08-3rd | 18,270 | 20,448 | 128,547 | 573.8 | 253.7 | 320.1 | 91.2 | 18.8 | 72.4 | |
6c | nug20 | 14,098 | 72,546 | 281,906 | 192.3 | 176.1 | 16.1 | 435.5 | 37.5 | 398.0 | |
6c | nug30 | 52,260 | 379,350 | 1,567,800 | 11,473.2 | 5125.2 | 6337.0 | 11.1 | 1400.5 | t | |
6d | pds-100 | 94,994 | 433,867 | 933,313 | 110.6 | 104.9 | 5.7 | 30.9 | 28.1 | 2.7 | |
6d | pds-60 | 54,289 | 285,112 | 617,497 | 39.5 | 37.7 | 1.8 | 16.5 | 15.4 | 1.1 | |
6e | rail2586 | 2463 | 909,940 | 7,901,059 | 259.0 | 258.6 | 0.4 | 15.3 | 12.7 | 2.7 | |
6e | rail4284 | 4176 | 1,090,526 | 11,174,639 | 370.7 | 369.9 | 0.8 | 32.9 | 29.7 | 3.2 | |
7 | dfl001 | 4325 | 9511 | 30,833 | 2.2 | 2.0 | 0.1 | 0.6 | 0.5 | 0.1 | |
7 | pilot87 | 1815 | 4420 | 70,035 | 1.6 | 1.6 | 0.0 | 0.4 | 0.3 | 0.2 | |
7 | qap15 | 5698 | 22,218 | 85,413 | 15.4 | 13.3 | 2.1 | 4.3 | 2.8 | 1.5 |
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Schork, L., Gondzio, J. Implementation of an interior point method with basis preconditioning. Math. Prog. Comp. 12, 603–635 (2020). https://doi.org/10.1007/s12532-020-00181-8
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DOI: https://doi.org/10.1007/s12532-020-00181-8