SDPA in arbitrary multiple precision.
2024-10-28: Performance improvements of approximately 20% achieved.
I verified build on Ubuntu 20.04
rm -rf sdpa-gmp
git clone https://github.com/nakatamaho/sdpa-gmp.git
cd sdpa-gmp
aclocal ; autoconf ; automake --add-missing
autoreconf --force --install
./configure --enable-openmp=yes --enable-shared=yes
make -j4
@INPROCEEDINGS{SDPA-GMP,
author={Nakata, Maho},
booktitle={2010 IEEE International Symposium on Computer-Aided Control System Design},
title={A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP, -QD and -DD.},
year={2010}, volume={}, number={},
pages={29-34},
doi={10.1109/CACSD.2010.5612693}
}
binary64 optimals are taken from https://github.com/vsdp/SDPLIB/blob/master/README.md .
| Problem | m | n | Optimal (binary64) | Optimal (GMP) |
|---|---|---|---|---|
| arch0 | 174 | 335 | 5.66517e-01 | 5.6651727321592959e-01 |
| arch2 | 174 | 335 | 6.71515e-01 | 6.7151540763990793e-01 |
| arch4 | 174 | 335 | 9.726274e-01 | 9.7262741740980893e-01 |
| arch8 | 174 | 335 | 7.05698e+00 | 7.0569800367002555e+00 |
| control1 | 21 | 15 | 1.778463e+01 | 1.7784626717523405e+01 |
| control2 | 66 | 30 | 8.300000e+00 | 8.2999999857902351e+00 |
| control3 | 136 | 45 | 1.363327e+01 | 1.3633266228377313e+01 |
| control4 | 231 | 60 | 1.979423e+01 | 1.9794230376537536e+01 |
| control5 | 351 | 75 | 1.68836e+01 | 1.6883599050955793e+01 |
| control6 | 496 | 90 | 3.73044e+01 | 3.7304412616333280e+01 |
| control7 | 666 | 105 | 2.06251e+01 | 2.0625072243801761e+01 |
| control8 | 861 | 120 | 2.0286e+01 | 2.0286360379531460e+01 |
| control9 | 1081 | 135 | 1.46754e+01 | 1.4675424692813939e+01 |
| control10 | 1326 | 150 | 3.8533e+01 | 3.8533032079581028e+01 |
| control11 | 1596 | 165 | 3.1959e+01 | 3.1958667450372498e+01 |
| eqaulG11 | 801 | 801 | 6.291553e+02 | 6.2915529282061428e+02 |
| equalG51 | 1001 | 1001 | 4.005601e+03 | 4.0056013154878550e+03 |
| gpp100 | 101 | 100 | -4.49435e+01 | -4.4943550775891146e+01 |
| gpp124-1 | 125 | 124 | -7.3431e+00 | -7.3430762652465377e+00 |
| gpp124-2 | 125 | 124 | -4.68623e+01 | -4.6862295072749908e+01 |
| gpp124-3 | 125 | 124 | -1.53014e+02 | -1.5301412730175306e+02 |
| gpp124-4 | 125 | 124 | -4.1899e+02 | -4.1898762587351130e+02 |
| gpp250-1 | 250 | 250 | -1.5445e+01 | -1.5444916882934067e+01 |
| gpp250-2 | 250 | 250 | -8.1869e+01 | -8.1868958840223643e+01 |
| gpp250-3 | 250 | 250 | -3.035e+02 | -3.0353932422884198e+02 |
| gpp250-4 | 250 | 250 | -7.473e+02 | -7.4732831101269269e+02 |
| gpp500-1 | 501 | 500 | -2.53e+01 | -2.5320543879075787e+01 |
| gpp500-2 | 501 | 500 | -1.5606e+02 | -1.5606038757941642e+02 |
| gpp500-3 | 501 | 500 | -5.1302e+02 | -5.1301760233182234e+02 |
| gpp500-4 | 501 | 500 | -1.56702e+03 | -1.5670187921561449e+03 |
| hinf1 | 13 | 14 | 2.0326e+00 | 2.6899806999311550e-05 |
| hinf2 | 13 | 16 | 1.0967e+01 | 1.0967055621049256e+01 |
| hinf3 | 13 | 16 | 5.69e+01 | 5.6940778009669388e+01 |
| hinf4 | 13 | 16 | 2.74764e+02 | 2.7149772617088246e+02 |
| hinf5 | 13 | 16 | 3.63e+02 | 3.3010372908768509e+02 |
| hinf6 | 13 | 16 | 4.490e+02 | 4.4892774532835125e+02 |
| hinf7 | 13 | 16 | 3.91e+02 | 1.5490470173390994e+02 |
| hinf8 | 13 | 16 | 1.16e+02 | 5.8449173799445524e+01 |
| hinf9 | 13 | 16 | 2.3625e+02 | 2.3624925825291886e+02 |
| hinf10 | 21 | 18 | 1.09e+02 | 1.3503382826378728e+01 |
| hinf11 | 31 | 22 | 6.59e+01 | 5.0979848897318626e+01 |
| hinf12 | 43 | 24 | 2e-1 | 1.5875842644916031e-13 |
| hinf13 | 57 | 30 | 4.6e+01 | 1.1816982963162776e-02 |
| hinf14 | 73 | 34 | 1.30e+01 | 2.8479790096215441e+00 |
| hinf15 | 91 | 37 | 2.5e+01 | 1.1224662755236866e-04 |
| infd1 | 10 | 30 | dual infeasible | -1.1641795380064849e+05 |
| infd2 | 10 | 30 | dual infeasible | -2.2856227327842922e+05 |
| infp1 | 10 | 30 | primal infeasible | 2.9943790805717583e+02 |
| infp2 | 10 | 30 | primal infeasible | 2.0749573188459872e+02 |
| maxG11 | 800 | 800 | 6.291648e+02 | 6.2916478300199902e+02 |
| maxG32 | 2000 | 2000 | 1.567640e+03 | 1.5676396446800114e+03 |
| maxG51 | 1000 | 1000 | 4.003809e+03 | 4.0062555216534127e+03 |
| maxG55 | 5000 | 5000 | 9.999210e+03 | - |
| maxG60 | 7000 | 7000 | 1.522227e+04 | - |
| mcp100 | 100 | 100 | 2.261574e+02 | 2.2615735148330884e+02 |
| mcp124-1 | 124 | 124 | 1.419905e+02 | 1.4199047709767370e+02 |
| mcp124-2 | 124 | 124 | 2.698802e+02 | 2.6988017064431990e+02 |
| mcp124-3 | 124 | 124 | 4.677501e+02 | 4.6775011428751099e+02 |
| mcp124-4 | 124 | 124 | 8.644119e+02 | 8.6441186405192719e+02 |
| mcp250-1 | 250 | 250 | 3.172643e+02 | 3.1726434034357982e+02 |
| mcp250-2 | 250 | 250 | 5.319301e+02 | 5.3193008393282009e+02 |
| mcp250-3 | 250 | 250 | 9.811726e+02 | 9.8117257166434770e+02 |
| mcp250-4 | 250 | 250 | 1.681960e+03 | 1.6819601121258921e+03 |
| mcp500-1 | 500 | 500 | 5.981485e+02 | 5.9814851691875962e+02 |
| mcp500-2 | 500 | 500 | 1.070057e+03 | 1.0700567662011862e+03 |
| mcp500-3 | 500 | 500 | 1.847970e+03 | 1.8479700215154574e+03 |
| mcp500-4 | 500 | 500 | 3.566738e+03 | 3.5667380499612209e+03 |
| qap5 | 136 | 26 | -4.360e+02 | -4.3600000000000000e+02 |
| qap6 | 229 | 37 | -3.8144e+02 | -3.8143840217367920e+02 |
| qap7 | 358 | 50 | -4.25e+02 | -4.2481971023200053e+02 |
| qap8 | 529 | 65 | -7.57e+02 | -7.5695525603861953e+02 |
| qap9 | 748 | 82 | -1.410e+03 | -1.4099410682401829e+03 |
| qap10 | 1021 | 101 | -1.093e+01 | -1.0926074684462390e+03 |
| qpG11 | 800 | 1600 | 2.448659e+03 | 2.4486591320079961e+03 |
| qpG51 | 1000 | 2000 | 1.181000e+03 | 1.1818000000000000e+04 |
| ss30 | 132 | 426 | 2.02395e+01 | 2.0239510569060567e+01 |
| theta1 | 104 | 50 | 2.300000e+01 | 2.3000000000000000e+01 |
| theta2 | 498 | 100 | 3.287917e+01 | 3.2879169015772581e+01 |
| theta3 | 1106 | 150 | 4.216698e+01 | 4.2166981488494406e+01 |
| theta4 | 1949 | 200 | 5.032122e+01 | 5.0321221951837344e+01 |
| theta5 | 3028 | 250 | 5.723231e+01 | 5.7232307282180003e+01 |
| theta6 | 4375 | 300 | 6.347709e+01 | 6.3477087177964743e+01 |
| thetaG11 | 2401 | 801 | 4.000000e+02 | 4.0000000000000000e+02 |
| thetaG51 | 6910 | 1001 | 3.49000e+02 | 3.4900000000000000e+02 |
| truss1 | 6 | 13 | -8.999996e+00 | -8.9999963152868905e+00 |
| truss2 | 58 | 133 | -1.233804e+02 | -1.2338035636407390e+02 |
| truss3 | 27 | 31 | -9.109996e+00 | -9.1099962092020534e+00 |
| truss4 | 12 | 19 | -9.009996e+00 | -9.0099962910045294e+00 |
| truss5 | 208 | 331 | -1.326357e+02 | -1.3263567797250604e+02 |
| truss6 | 172 | 451 | -9.01001e+02 | -9.0100140477088096e+02 |
| truss7 | 86 | 301 | -9.00001e+02 | -9.0000140369343463e+02 |
| truss8 | 496 | 628 | -1.331146e+02 | -1.3311458915226341e+02 |