{"id":403,"date":"2021-03-15T14:36:17","date_gmt":"2021-03-15T18:36:17","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/hager\/?page_id=403"},"modified":"2026-03-19T08:18:25","modified_gmt":"2026-03-19T12:18:25","slug":"objective-value-comparisons-for-netlib-test-problems","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/hager\/objective-value-comparisons-for-netlib-test-problems\/","title":{"rendered":"Objective value comparisons for Netlib test problems"},"content":{"rendered":"\r\n
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Objective value comparisons for Netlib test problems<\/h1>\n\n\n\n

Comparisons are given for the cost values gotten by running the LP DASA
\ncode to the cost values archived in the Netlib LP directory. The stopping
\ncriterion for LP DASA, as discussed in the paper “A sparse proximal
\nimplementation of the LP Dual Active Set Algorithm,” was based in the
\nrelative error in the optimality conditions. The results given below
\ncorrespond to relative errors of 10^{-8} and 10^{-12}. The Netlib
\nobjective function values appearing in column 4 below are the values
\nappearing at the top of the Netlib file, with the following exceptions:
\nThe CPLEX values for some problems, given by Bob Bixby later in the file,
\nare used in place of the original values. Also, the values given for the
\nfollowing problems, which appear to have 6 or 7 digit accuracy, are replaced
\nby more accurate values obtained using CPLEX: FINNIS, D2Q06C, and PILOT87.<\/p>\n\n\n\n\n\n

Generally, the 10^{-8} criterion yields more than 8 significant digits
\nin the cost. Note though that for the 16 problems of Jeffrey Kennington,
\nonly 8 digits are reported, so it is only possible to match these 8 digits.<\/p>\n\n\n\n\n\n

As a group, the pilot problems (including PEROLD) and the 10^{-8} criterion
\nyield the poorest agreement with the archived cost. The agreement ranges
\nbetween 4 and 11 significant digits.<\/p>\n\n\n\n\n\n

The worst agreement with the archived objective function values
\noccurs with GREENBEA for which there were only 3 significant digits with
\nthe 10^{-8} stopping criterion. When the error tolerance was reduced
\nto 10^{-12}, the agreement increased to the 8th significant digit.
\nIn fact, the LP DASA cost was better than the archived cost in the 8th digit:<\/p>\n\n\n\n\n\n

LP DASA, GREENBEA, 10^{-12} tolerance, value = -7.25552503916e+07<\/p>\n\n\n\n\n\n

The associated relative errors in the primal and dual residuals were
\n2.49e-13 and 5.97e-14.<\/p>\n\n\n\n\n\n

The second worst agreement with the archived objected function values occurs
\nwith FFFFF800 for which there were only 4 significant digits with the 10^{-8}
\nstopping criterion. When the error tolerance was reduced to 10^{-12}, the
\nagreement increased to the 11 digits listed in the Netlib archive.<\/p>\n\n\n\n\n\n

Digits is given by the formula: floor (.5 – log10 (abs(netlib – lpdasa)\/abs (netlib)))
\n===========================================================================================================================
\n Netlib LP DASA LP DASA Relative Relative
\nName Rows Cols Nonzeros Optimal Value Optimal Value Digits Optimal Value b-err c-err Digits
\n 10^(-8) Tol 10^(-12) Tol
\n25FV47 822 1571 11127 5.5018458883E+03 5.5018458836e+03 (09) 5.50184588829e+03 1.01e-14 2.87e-18 (12)
\n80BAU3B 2263 9799 29063 9.8722419241E+05 9.8722418531e+05 (08) 9.87224192409e+05 2.84e-16 3.67e-18 (12)
\nADLITTLE 57 97 465 2.2549496316E+05 2.2549496302e+05 (09) 2.25494963163e+05 8.90e-14 1.02e-17 (11)
\nAFIRO 28 32 88 -4.6475314286E+02 -4.6475314286e+02 (11) -4.64753142857e+02 3.59e-14 2.95e-17 (11)
\nAGG 489 163 2541 -3.5991767287E+07 -3.5991769285e+07 (07) -3.59917672878e+07 1.27e-14 7.98e-19 (11)
\nAGG2 517 302 4515 -2.0239252356E+07 -2.0239252356e+07 (11) -2.02392523560e+07 1.94e-19 3.31e-20 (12)
\nAGG3 517 302 4531 1.0312115935E+07 1.0312115935e+07 (12) 1.03121159351e+07 1.04e-18 2.26e-19 (11)
\nBANDM 306 472 2659 -1.5862801845E+02 -1.5862801847e+02 (10) -1.58628018450e+02 3.79e-20 1.53e-16 (12)
\nBEACONFD 174 262 3476 3.3592485807E+04 3.3592485817e+04 (10) 3.35924858072e+04 9.01e-22 2.59e-18 (11)
\nBLEND 75 83 521 -3.0812149846E+01 -3.0812149846e+01 (11) -3.08121498458e+01 7.11e-22 3.06e-16 (11)
\nBNL1 644 1175 6129 1.9776295615E+03 1.9776295615e+03 (11) 1.97762956152e+03 4.65e-13 2.03e-18 (11)
\nBNL2 2325 3489 16124 1.8112365404E+03 1.8112367470e+03 (07) 1.81123654036e+03 4.50e-15 4.01e-18 (11)
\nBORE3D 234 315 1525 1.3730803942E+03 1.3730803942e+03 (11) 1.37308039421e+03 2.04e-16 1.52e-19 (11)
\nBRANDY 221 249 2150 1.5185098965E+03 1.5185098965e+03 (11) 1.51850989649e+03 2.61e-20 1.23e-20 (11)
\nCAPRI 272 353 1786 2.6900129138E+03 2.6900131064e+03 (07) 2.69001291377e+03 9.18e-16 5.37e-19 (11)
\nCRE-A 3517 4067 19054 2.3595407e+07 2.3595407434e+07 (08) 2.35954070610e+07 1.02e-15 3.61e-20 (09)
\nCRE-B 9649 72447 328542 2.3129640e+07 2.3129639887e+07 (08) 2.31296398868e+07 5.21e-13 3.24e-18 (08)
\nCRE-C 3069 3678 16922 2.5275116e+07 2.5275116153e+07 (08) 2.52751161409e+07 4.52e-13 1.16e-18 (08)
\nCRE-D 8927 69980 312626 2.4454970e+07 2.4454969890e+07 (08) 2.44549697645e+07 4.32e-13 3.70e-19 (08)
\nCYCLE 1904 2857 21322 -5.2263930249E+00 -5.2263930249e+00 (12) -5.22639302489e+00 3.54e-13 2.54e-17 (12)
\nCZPROB 930 3523 14173 2.1851966989E+06 2.1851966987e+06 (10) 2.18519669886e+06 2.41e-14 5.47e-15 (11)
\nD2Q06C 2172 5167 35674 1.2278421081e+05 1.2278421081e+05 (10) 1.22784210814e+05 3.61e-16 3.30e-17 (10)
\nD6CUBE 416 6184 43888 3.1549166667E+02 3.1549166667e+02 (11) 3.15491666667e+02 4.84e-14 4.02e-16 (11)
\nDEGEN2 445 534 4449 -1.4351780000E+03 -1.4351779999e+03 (10) -1.43517800000e+03 1.17e-16 5.14e-18 (16)
\nDEGEN3 1504 1818 26230 -9.8729400000E+02 -9.8729399999e+02 (11) -9.87294000000e+02 3.63e-17 5.03e-15 (16)
\nDFL001 6072 12230 41873 1.1266396047E+07 1.1266566641e+07 (05) 1.12663960467e+07 1.77e-16 1.84e-18 (11)
\nE226 224 282 2767 -1.8751929066E+01 -1.8751929067e+01 (10) -1.87519290664e+01 2.26e-14 1.77e-17 (11)
\nETAMACRO 401 688 2489 -7.5571523337E+02 -7.5571523112e+02 (09) -7.55715233357e+02 1.75e-19 7.81e-13 (11)
\nFFFFF800 525 854 6235 5.5567956482E+05 5.5571575854e+05 (04) 5.55679564817e+05 2.81e-13 7.01e-18 (11)
\nFINNIS 498 614 2714 1.7279106560e+05 1.7279106512e+05 (09) 1.72791065596e+05 2.85e-13 2.14e-19 (11)
\nFIT1D 25 1026 14430 -9.1463780924E+03 -9.1463780909e+03 (10) -9.14637809242e+03 1.82e-20 1.51e-15 (12)
\nFIT1P 628 1677 10894 9.1463780924E+03 9.1463780924e+03 (12) 9.14637809242e+03 1.49e-21 2.32e-15 (12)
\nFIT2D 26 10500 138018 -6.8464293294E+04 -6.8464293294e+04 (12) -6.84642932938e+04 3.45e-21 3.58e-16 (12)
\nFIT2P 3001 13525 60784 6.8464293232E+04 6.8464293294e+04 (09) 6.84642932938e+04 1.02e-19 2.53e-14 (09)
\nGANGES 1310 1681 7021 -1.0958573613E+05 -1.0958573613e+05 (11) -1.09585736129e+05 8.25e-15 1.57e-15 (11)
\nGFRD-PNC 617 1092 3467 6.9022359995E+06 6.9022359731e+06 (08) 6.90223599955e+06 4.12e-19 2.58e-15 (11)
\nGREENBEA 2393 5405 31499 -7.2555248130E+07 -7.2462440347e+07 (03) -7.25552503916e+07 2.49e-13 5.97e-14 (08)
\nGREENBEB 2393 5405 31499 -4.3022602612E+06 -4.3022602608e+06 (10) -4.30226026121e+06 3.15e-13 3.12e-18 (12)
\nGROW15 301 645 5665 -1.0687094129E+08 -1.0687094129e+08 (10) -1.06870941294e+08 9.68e-14 2.85e-17 (10)
\nGROW22 441 946 8318 -1.6083433648E+08 -1.6083433648e+08 (11) -1.60834336483e+08 5.62e-14 1.58e-17 (11)
\nGROW7 141 301 2633 -4.7787811815E+07 -4.7787811815e+07 (11) -4.77878118147e+07 4.25e-14 1.94e-17 (11)
\nISRAEL 175 142 2358 -8.9664482186E+05 -8.9664482186e+05 (11) -8.96644821863e+05 1.10e-14 9.58e-19 (11)
\nKB2 44 41 291 -1.7499001299E+03 -1.7499001299e+03 (11) -1.74990012991e+03 4.21e-17 1.24e-13 (11)
\nKEN-07 2427 3602 11981 -6.7952044e+08 -6.7952044339e+08 (08) -6.79520443382e+08 3.45e-18 1.97e-15 (08)
\nKEN-11 14695 21349 70354 -6.9723823e+09 -6.9723822625e+09 (08) -6.97238226252e+09 6.84e-18 2.02e-17 (08)
\nKEN-13 28633 42659 139834 -1.0257395e+10 -1.0257394789e+10 (08) -1.02573947895e+10 1.78e-16 9.76e-18 (08)
\nKEN-18 105128 154699 512719 -5.2217025e+10 -5.2217025287e+10 (08) -5.22170252874e+10 5.68e-17 5.22e-15 (08)
\nLOTFI 154 308 1086 -2.5264706062E+01 -2.5264706062e+01 (11) -2.52647060615e+01 7.36e-15 1.95e-18 (11)
\nMAROS 847 1443 10006 -5.8063743701E+04 -5.8063743701e+04 (12) -5.80637437011e+04 1.12e-13 1.52e-20 (12)
\nMAROS-R7 3137 9408 151120 1.4971851665E+06 1.4971851665e+06 (11) 1.49718516648e+06 3.25e-22 9.07e-17 (11)
\nMODSZK1 688 1620 4158 3.2061972906E+02 3.2061972909e+02 (10) 3.20619729090e+02 3.54e-17 8.33e-15 (10)
\nOSA-07 1119 23949 167643 5.3572252e+05 5.3572251730e+05 (08) 5.35722517299e+05 1.39e-17 3.90e-18 (08)
\nOSA-14 2338 52460 367220 1.1064628e+06 1.1064628449e+06 (07) 1.10646284474e+06 3.47e-17 4.99e-18 (07)
\nOSA-30 4351 100024 700160 2.1421399e+06 2.1421398738e+06 (08) 2.14213987321e+06 5.84e-18 5.44e-18 (08)
\nOSA-60 10281 232966 1630758 4.0440725e+06 4.0440725055e+06 (09) 4.04407250316e+06 3.47e-17 7.32e-18 (09)
\nPDS-02 2954 7535 21252 2.8857862e+10 2.8857862010e+10 (09) 2.88578620100e+10 1.40e-15 9.05e-19 (09)
\nPDS-06 9882 28655 82269 2.7761038e+10 2.7761037600e+10 (08) 2.77610376000e+10 1.39e-13 1.85e-16 (08)
\nPDS-10 16559 48763 140063 2.6727095e+10 2.6727094976e+10 (09) 2.67270949760e+10 2.51e-15 8.07e-14 (09)
\nPDS-20 33875 105728 304153 2.3821659e+10 2.3821658640e+10 (08) 2.38216586400e+10 6.15e-14 4.63e-15 (08)
\nPEROLD 626 1376 6026 -9.3807552782E+03 -9.3807578160e+03 (07) -9.38075527829e+03 4.09e-15 5.80e-19 (11)
\nPILOT 1442 3652 43220 -5.5748972928E+02 -5.5747482669e+02 (05) -5.57489729284e+02 1.37e-18 1.45e-17 (11)
\nPILOT.JA 941 1988 14706 -6.1131364656E+03 -6.1131345861e+03 (07) -6.11313646558e+03 8.50e-15 6.12e-13 (12)
\nPILOT.WE 723 2789 9218 -2.7201075328E+06 -2.7199466997e+06 (04) -2.72010753286e+06 2.86e-16 6.21e-13 (11)
\nPILOT4 411 1000 5145 -2.5811392589E+03 -2.5811375521e+03 (06) -2.58113925888e+03 1.15e-21 1.38e-13 (11)
\nPILOT87 2031 4883 73804 3.0171034733E+02 3.0171062422e+02 (06) 3.01710347333e+02 2.01e-15 7.59e-14 (11)
\nPILOTNOV 976 2172 13129 -4.4972761882E+03 -4.4972761882e+03 (11) -4.49727618822e+03 4.56e-15 4.52e-15 (11)
\nQAP8 913 1632 8304 2.0350000000E+02 2.0350000000e+02 (15) 2.03500000000e+02 4.51e-14 8.00e-17 (14)
\nQAP12 3193 8856 44244 5.2289435056E+02 5.2289435056e+02 (12) 5.22894350559e+02 1.58e-13 3.30e-18 (12)
\nQAP15 6331 22275 110700 1.0409940410E+03 1.0409940410e+03 (10) 1.04099404096e+03 4.62e-13 4.66e-18 (10)
\nRECIPE 92 180 752 -2.6661600000E+02 -2.6661600000e+02 (11) -2.66616000000e+02 6.94e-18 2.50e-17 (15)
\nSC105 106 103 281 -5.2202061212E+01 -5.2202060187e+01 (08) -5.22020612117e+01 2.82e-20 2.95e-15 (11)
\nSC205 206 203 552 -5.2202061212E+01 -5.2202061212e+01 (11) -5.22020612117e+01 1.15e-14 3.36e-15 (11)
\nSC50A 51 48 131 -6.4575077059E+01 -6.4575077038e+01 (09) -6.45750770586e+01 3.20e-17 7.87e-16 (11)
\nSC50B 51 48 119 -7.0000000000E+01 -6.9999999978e+01 (09) -7.00000000000e+01 1.04e-22 3.78e-15 (16)
\nSCAGR25 472 500 2029 -1.4753433061E+07 -1.4753433082e+07 (09) -1.47534330608e+07 6.32e-20 1.79e-16 (11)
\nSCAGR7 130 140 553 -2.3313898243E+06 -2.3313898234e+06 (09) -2.33138982433e+06 7.23e-20 1.40e-17 (11)
\nSCFXM1 331 457 2612 1.8416759028E+04 1.8416759028e+04 (11) 1.84167590283e+04 6.36e-14 3.26e-17 (11)
\nSCFXM2 661 914 5229 3.6660261565E+04 3.6660261565e+04 (12) 3.66602615650e+04 7.37e-15 8.60e-18 (13)
\nSCFXM3 991 1371 7846 5.4901254550E+04 5.4901254550e+04 (11) 5.49012545498e+04 6.96e-15 8.60e-18 (11)
\nSCORPION 389 358 1708 1.8781248227E+03 1.8781248227e+03 (11) 1.87812482274e+03 6.73e-18 2.72e-19 (11)
\nSCRS8 491 1169 4029 9.0429695380E+02 9.0429695380e+02 (12) 9.04296953801e+02 8.34e-17 2.75e-22 (12)
\nSCSD1 78 760 3148 8.6666666743E+00 8.6666666743e+00 (11) 8.66666667433e+00 5.73e-14 1.77e-15 (11)
\nSCSD6 148 1350 5666 5.0500000077E+01 5.0500000078e+01 (11) 5.05000000771e+01 7.28e-16 4.63e-18 (12)
\nSCSD8 398 2750 11334 9.0499999993E+02 9.0500000097e+02 (09) 9.04999999925e+02 2.14e-14 2.30e-13 (11)
\nSCTAP1 301 480 2052 1.4122500000E+03 1.4122500000e+03 (15) 1.41225000000e+03 1.74e-14 2.34e-18 (14)
\nSCTAP2 1091 1880 8124 1.7248071429E+03 1.7248071429e+03 (11) 1.72480714286e+03 8.94e-14 9.28e-18 (11)
\nSCTAP3 1481 2480 10734 1.4240000000E+03 1.4240000000e+03 (14) 1.42400000000e+03 3.84e-14 1.58e-17 (14)
\nSHARE1B 118 225 1182 -7.6589318579E+04 -7.6589318579e+04 (12) -7.65893185792e+04 4.74e-19 3.86e-16 (12)
\nSHARE2B 97 79 730 -4.1573224074E+02 -4.1573223926e+02 (08) -4.15732240741e+02 3.22e-17 3.63e-15 (11)
\nSHELL 537 1775 4900 1.2088253460E+09 1.2088253460e+09 (11) 1.20882534600e+09 6.37e-17 2.10e-16 (16)
\nSHIP04L 403 2118 8450 1.7933245380E+06 1.7933245379e+06 (10) 1.79332453797e+06 5.66e-23 8.05e-17 (11)
\nSHIP04S 403 1458 5810 1.7987147004E+06 1.7987147001e+06 (10) 1.79871470045e+06 9.16e-21 1.32e-15 (11)
\nSHIP08L 779 4283 17085 1.9090552114E+06 1.9090552115e+06 (10) 1.90905521139e+06 4.13e-21 1.66e-15 (11)
\nSHIP08S 779 2387 9501 1.9200982105E+06 1.9200982105e+06 (11) 1.92009821053e+06 1.21e-22 6.77e-17 (11)
\nSHIP12L 1152 5427 21597 1.4701879193E+06 1.4701879194e+06 (10) 1.47018791933e+06 3.71e-18 1.33e-16 (11)
\nSHIP12S 1152 2763 10941 1.4892361344E+06 1.4892361344e+06 (11) 1.48923613441e+06 1.97e-16 5.32e-16 (11)
\nSIERRA 1228 2036 9252 1.5394362184E+07 1.5394362206e+07 (09) 1.53943621836e+07 6.32e-17 1.73e-18 (11)
\nSTAIR 357 467 3857 -2.5126695119E+02 -2.5126695389e+02 (08) -2.51266951193e+02 1.25e-22 4.14e-20 (11)
\nSTANDATA 360 1075 3038 1.2576995000E+03 1.2576995000e+03 (11) 1.25769950000e+03 3.86e-15 2.57e-15 (16)
\nSTANDMPS 468 1075 3686 1.4060175000E+03 1.4060175000e+03 (16) 1.40601750000e+03 1.51e-13 7.36e-15 (12)
\nSTOCFOR1 118 111 474 -4.1131976219E+04 -4.1131976734e+04 (08) -4.11319762194e+04 1.93e-18 6.52e-15 (11)
\nSTOCFOR2 2158 2031 9492 -3.9024408538E+04 -3.9024408608e+04 (09) -3.90244085379e+04 1.37e-17 4.36e-15 (12)
\nSTOCFOR3 16676 15695 74004 -3.9976783944E+04 -3.9976783941e+04 (10) -3.99767839436e+04 3.37e-17 5.79e-21 (11)
\nTRUSS 1001 8806 36642 4.5881584719E+05 4.5881584719e+05 (11) 4.58815847186e+05 3.71e-17 2.13e-18 (11)
\nTUFF 334 587 4523 2.9214776509E-01 2.9214776505e-01 (10) 2.92147765094e-01 1.52e-14 8.41e-15 (11)
\nVTP.BASE 199 203 914 1.2983146246E+05 1.2983146243e+05 (10) 1.29831462461e+05 3.01e-19 6.95e-18 (11)
\nWOOD1P 245 2594 70216 1.4429024116E+00 1.4429024184e+00 (08) 1.44290241157e+00 1.42e-13 3.96e-17 (11)
\nWOODW 1099 8405 37478 1.3044763331E+00 1.3044763350e+00 (09) 1.30447633308e+00 2.07e-13 6.95e-15 (11)<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1075,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-403","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/403","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/users\/1075"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/comments?post=403"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/403\/revisions"}],"predecessor-version":[{"id":791,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/403\/revisions\/791"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/media?parent=403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}