MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance dtoc5
A discrete time optimal control (DTOC) problem with 50000 time periods, 1 control variable, and 1 state variable. Problem 5 in Coleman and Liao (1995)
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.00243096 (BARON) 0.00237817 (COUENNE) 0.00062677 (SCIP) |
| Referencesⓘ | Coleman, Thomas F. and Liao, Aiping, An efficient trust region method for unconstrained discrete-time optimal control problems, Computational Optimization and Applications, 4:1, 1995, 47-66. |
| Sourceⓘ | QPLIB instance 8585, contributed by Nick Gould, CUTEr model DTOC5 |
| Applicationⓘ | Optimal Control |
| Added to libraryⓘ | 18 Aug 2018 |
| Problem typeⓘ | QCQP |
| #Variablesⓘ | 99999 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 99998 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 99998 |
| #Nonlinear Nonzeros in Objectiveⓘ | 99998 |
| #Constraintsⓘ | 49999 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 49999 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 149997 |
| #Nonlinear Nonzeros in Jacobianⓘ | 49999 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 99998 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 99998 |
| #Blocks in Hessian of Lagrangianⓘ | 99998 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.0000e-05 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 50000 50000 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 100000 100000 0 0 0 0 0 0
* FX 1
*
* Nonzero counts
* Total const NL DLL
* 249996 99999 149997 0
*
* Solve m using QCP minimizing objvar;
Variables objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
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,x99828,x99829,x99830,x99831,x99832,x99833,x99834,x99835,x99836
,x99837,x99838,x99839,x99840,x99841,x99842,x99843,x99844,x99845
,x99846,x99847,x99848,x99849,x99850,x99851,x99852,x99853,x99854
,x99855,x99856,x99857,x99858,x99859,x99860,x99861,x99862,x99863
,x99864,x99865,x99866,x99867,x99868,x99869,x99870,x99871,x99872
,x99873,x99874,x99875,x99876,x99877,x99878,x99879,x99880,x99881
,x99882,x99883,x99884,x99885,x99886,x99887,x99888,x99889,x99890
,x99891,x99892,x99893,x99894,x99895,x99896,x99897,x99898,x99899
,x99900,x99901,x99902,x99903,x99904,x99905,x99906,x99907,x99908
,x99909,x99910,x99911,x99912,x99913,x99914,x99915,x99916,x99917
,x99918,x99919,x99920,x99921,x99922,x99923,x99924,x99925,x99926
,x99927,x99928,x99929,x99930,x99931,x99932,x99933,x99934,x99935
,x99936,x99937,x99938,x99939,x99940,x99941,x99942,x99943,x99944
,x99945,x99946,x99947,x99948,x99949,x99950,x99951,x99952,x99953
,x99954,x99955,x99956,x99957,x99958,x99959,x99960,x99961,x99962
,x99963,x99964,x99965,x99966,x99967,x99968,x99969,x99970,x99971
,x99972,x99973,x99974,x99975,x99976,x99977,x99978,x99979,x99980
,x99981,x99982,x99983,x99984,x99985,x99986,x99987,x99988,x99989
,x99990,x99991,x99992,x99993,x99994,x99995,x99996,x99997,x99998
,x99999,x100000;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295,e296,e297,e298
,e299,e300,e301,e302,e303,e304,e305,e306,e307,e308,e309,e310,e311
,e312,e313,e314,e315,e316,e317,e318,e319,e320,e321,e322,e323,e324
,e325,e326,e327,e328,e329,e330,e331,e332,e333,e334,e335,e336,e337
,e338,e339,e340,e341,e342,e343,e344,e345,e346,e347,e348,e349,e350
,e351,e352,e353,e354,e355,e356,e357,e358,e359,e360,e361,e362,e363
,e364,e365,e366,e367,e368,e369,e370,e371,e372,e373,e374,e375,e376
,e377,e378,e379,e380,e381,e382,e383,e384,e385,e386,e387,e388,e389
,e390,e391,e392,e393,e394,e395,e396,e397,e398,e399,e400,e401,e402
,e403,e404,e405,e406,e407,e408,e409,e410,e411,e412,e413,e414,e415
,e416,e417,e418,e419,e420,e421,e422,e423,e424,e425,e426,e427,e428
,e429,e430,e431,e432,e433,e434,e435,e436,e437,e438,e439,e440,e441
,e442,e443,e444,e445,e446,e447,e448,e449,e450,e451,e452,e453,e454
,e455,e456,e457,e458,e459,e460,e461,e462,e463,e464,e465,e466,e467
,e468,e469,e470,e471,e472,e473,e474,e475,e476,e477,e478,e479,e480
,e481,e482,e483,e484,e485,e486,e487,e488,e489,e490,e491,e492,e493
,e494,e495,e496,e497,e498,e499,e500,e501,e502,e503,e504,e505,e506
,e507,e508,e509,e510,e511,e512,e513,e514,e515,e516,e517,e518,e519
,e520,e521,e522,e523,e524,e525,e526,e527,e528,e529,e530,e531,e532
,e533,e534,e535,e536,e537,e538,e539,e540,e541,e542,e543,e544,e545
,e546,e547,e548,e549,e550,e551,e552,e553,e554,e555,e556,e557,e558
,e559,e560,e561,e562,e563,e564,e565,e566,e567,e568,e569,e570,e571
,e572,e573,e574,e575,e576,e577,e578,e579,e580,e581,e582,e583,e584
,e585,e586,e587,e588,e589,e590,e591,e592,e593,e594,e595,e596,e597
,e598,e599,e600,e601,e602,e603,e604,e605,e606,e607,e608,e609,e610
,e611,e612,e613,e614,e615,e616,e617,e618,e619,e620,e621,e622,e623
,e624,e625,e626,e627,e628,e629,e630,e631,e632,e633,e634,e635,e636
,e637,e638,e639,e640,e641,e642,e643,e644,e645,e646,e647,e648,e649
,e650,e651,e652,e653,e654,e655,e656,e657,e658,e659,e660,e661,e662
,e663,e664,e665,e666,e667,e668,e669,e670,e671,e672,e673,e674,e675
,e676,e677,e678,e679,e680,e681,e682,e683,e684,e685,e686,e687,e688
,e689,e690,e691,e692,e693,e694,e695,e696,e697,e698,e699,e700,e701
,e702,e703,e704,e705,e706,e707,e708,e709,e710,e711,e712,e713,e714
,e715,e716,e717,e718,e719,e720,e721,e722,e723,e724,e725,e726,e727
,e728,e729,e730,e731,e732,e733,e734,e735,e736,e737,e738,e739,e740
,e741,e742,e743,e744,e745,e746,e747,e748,e749,e750,e751,e752,e753
,e754,e755,e756,e757,e758,e759,e760,e761,e762,e763,e764,e765,e766
,e767,e768,e769,e770,e771,e772,e773,e774,e775,e776,e777,e778,e779
,e780,e781,e782,e783,e784,e785,e786,e787,e788,e789,e790,e791,e792
,e793,e794,e795,e796,e797,e798,e799,e800,e801,e802,e803,e804,e805
,e806,e807,e808,e809,e810,e811,e812,e813,e814,e815,e816,e817,e818
,e819,e820,e821,e822,e823,e824,e825,e826,e827,e828,e829,e830,e831
,e832,e833,e834,e835,e836,e837,e838,e839,e840,e841,e842,e843,e844
,e845,e846,e847,e848,e849,e850,e851,e852,e853,e854,e855,e856,e857
,e858,e859,e860,e861,e862,e863,e864,e865,e866,e867,e868,e869,e870
,e871,e872,e873,e874,e875,e876,e877,e878,e879,e880,e881,e882,e883
,e884,e885,e886,e887,e888,e889,e890,e891,e892,e893,e894,e895,e896
,e897,e898,e899,e900,e901,e902,e903,e904,e905,e906,e907,e908,e909
,e910,e911,e912,e913,e914,e915,e916,e917,e918,e919,e920,e921,e922
,e923,e924,e925,e926,e927,e928,e929,e930,e931,e932,e933,e934,e935
,e936,e937,e938,e939,e940,e941,e942,e943,e944,e945,e946,e947,e948
,e949,e950,e951,e952,e953,e954,e955,e956,e957,e958,e959,e960,e961
,e962,e963,e964,e965,e966,e967,e968,e969,e970,e971,e972,e973,e974
,e975,e976,e977,e978,e979,e980,e981,e982,e983,e984,e985,e986,e987
,e988,e989,e990,e991,e992,e993,e994,e995,e996,e997,e998,e999,e1000
,e1001,e1002,e1003,e1004,e1005,e1006,e1007,e1008,e1009,e1010,e1011
,e1012,e1013,e1014,e1015,e1016,e1017,e1018,e1019,e1020,e1021,e1022
,e1023,e1024,e1025,e1026,e1027,e1028,e1029,e1030,e1031,e1032,e1033
,e1034,e1035,e1036,e1037,e1038,e1039,e1040,e1041,e1042,e1043,e1044
,e1045,e1046,e1047,e1048,e1049,e1050,e1051,e1052,e1053,e1054,e1055
,e1056,e1057,e1058,e1059,e1060,e1061,e1062,e1063,e1064,e1065,e1066
,e1067,e1068,e1069,e1070,e1071,e1072,e1073,e1074,e1075,e1076,e1077
,e1078,e1079,e1080,e1081,e1082,e1083,e1084,e1085,e1086,e1087,e1088
,e1089,e1090,e1091,e1092,e1093,e1094,e1095,e1096,e1097,e1098,e1099
,e1100,e1101,e1102,e1103,e1104,e1105,e1106,e1107,e1108,e1109,e1110
,e1111,e1112,e1113,e1114,e1115,e1116,e1117,e1118,e1119,e1120,e1121
,e1122,e1123,e1124,e1125,e1126,e1127,e1128,e1129,e1130,e1131,e1132
,e1133,e1134,e1135,e1136,e1137,e1138,e1139,e1140,e1141,e1142,e1143
,e1144,e1145,e1146,e1147,e1148,e1149,e1150,e1151,e1152,e1153,e1154
,e1155,e1156,e1157,e1158,e1159,e1160,e1161,e1162,e1163,e1164,e1165
,e1166,e1167,e1168,e1169,e1170,e1171,e1172,e1173,e1174,e1175,e1176
,e1177,e1178,e1179,e1180,e1181,e1182,e1183,e1184,e1185,e1186,e1187
,e1188,e1189,e1190,e1191,e1192,e1193,e1194,e1195,e1196,e1197,e1198
,e1199,e1200,e1201,e1202,e1203,e1204,e1205,e1206,e1207,e1208,e1209
,e1210,e1211,e1212,e1213,e1214,e1215,e1216,e1217,e1218,e1219,e1220
,e1221,e1222,e1223,e1224,e1225,e1226,e1227,e1228,e1229,e1230,e1231
,e1232,e1233,e1234,e1235,e1236,e1237,e1238,e1239,e1240,e1241,e1242
,e1243,e1244,e1245,e1246,e1247,e1248,e1249,e1250,e1251,e1252,e1253
,e1254,e1255,e1256,e1257,e1258,e1259,e1260,e1261,e1262,e1263,e1264
,e1265,e1266,e1267,e1268,e1269,e1270,e1271,e1272,e1273,e1274,e1275
,e1276,e1277,e1278,e1279,e1280,e1281,e1282,e1283,e1284,e1285,e1286
,e1287,e1288,e1289,e1290,e1291,e1292,e1293,e1294,e1295,e1296,e1297
,e1298,e1299,e1300,e1301,e1302,e1303,e1304,e1305,e1306,e1307,e1308
,e1309,e1310,e1311,e1312,e1313,e1314,e1315,e1316,e1317,e1318,e1319
,e1320,e1321,e1322,e1323,e1324,e1325,e1326,e1327,e1328,e1329,e1330
,e1331,e1332,e1333,e1334,e1335,e1336,e1337,e1338,e1339,e1340,e1341
,e1342,e1343,e1344,e1345,e1346,e1347,e1348,e1349,e1350,e1351,e1352
,e1353,e1354,e1355,e1356,e1357,e1358,e1359,e1360,e1361,e1362,e1363
,e1364,e1365,e1366,e1367,e1368,e1369,e1370,e1371,e1372,e1373,e1374
,e1375,e1376,e1377,e1378,e1379,e1380,e1381,e1382,e1383,e1384,e1385
,e1386,e1387,e1388,e1389,e1390,e1391,e1392,e1393,e1394,e1395,e1396
,e1397,e1398,e1399,e1400,e1401,e1402,e1403,e1404,e1405,e1406,e1407
,e1408,e1409,e1410,e1411,e1412,e1413,e1414,e1415,e1416,e1417,e1418
,e1419,e1420,e1421,e1422,e1423,e1424,e1425,e1426,e1427,e1428,e1429
,e1430,e1431,e1432,e1433,e1434,e1435,e1436,e1437,e1438,e1439,e1440
,e1441,e1442,e1443,e1444,e1445,e1446,e1447,e1448,e1449,e1450,e1451
,e1452,e1453,e1454,e1455,e1456,e1457,e1458,e1459,e1460,e1461,e1462
,e1463,e1464,e1465,e1466,e1467,e1468,e1469,e1470,e1471,e1472,e1473
,e1474,e1475,e1476,e1477,e1478,e1479,e1480,e1481,e1482,e1483,e1484
,e1485,e1486,e1487,e1488,e1489,e1490,e1491,e1492,e1493,e1494,e1495
,e1496,e1497,e1498,e1499,e1500,e1501,e1502,e1503,e1504,e1505,e1506
,e1507,e1508,e1509,e1510,e1511,e1512,e1513,e1514,e1515,e1516,e1517
,e1518,e1519,e1520,e1521,e1522,e1523,e1524,e1525,e1526,e1527,e1528
,e1529,e1530,e1531,e1532,e1533,e1534,e1535,e1536,e1537,e1538,e1539
,e1540,e1541,e1542,e1543,e1544,e1545,e1546,e1547,e1548,e1549,e1550
,e1551,e1552,e1553,e1554,e1555,e1556,e1557,e1558,e1559,e1560,e1561
,e1562,e1563,e1564,e1565,e1566,e1567,e1568,e1569,e1570,e1571,e1572
,e1573,e1574,e1575,e1576,e1577,e1578,e1579,e1580,e1581,e1582,e1583
,e1584,e1585,e1586,e1587,e1588,e1589,e1590,e1591,e1592,e1593,e1594
,e1595,e1596,e1597,e1598,e1599,e1600,e1601,e1602,e1603,e1604,e1605
,e1606,e1607,e1608,e1609,e1610,e1611,e1612,e1613,e1614,e1615,e1616
,e1617,e1618,e1619,e1620,e1621,e1622,e1623,e1624,e1625,e1626,e1627
,e1628,e1629,e1630,e1631,e1632,e1633,e1634,e1635,e1636,e1637,e1638
,e1639,e1640,e1641,e1642,e1643,e1644,e1645,e1646,e1647,e1648,e1649
,e1650,e1651,e1652,e1653,e1654,e1655,e1656,e1657,e1658,e1659,e1660
,e1661,e1662,e1663,e1664,e1665,e1666,e1667,e1668,e1669,e1670,e1671
,e1672,e1673,e1674,e1675,e1676,e1677,e1678,e1679,e1680,e1681,e1682
,e1683,e1684,e1685,e1686,e1687,e1688,e1689,e1690,e1691,e1692,e1693
,e1694,e1695,e1696,e1697,e1698,e1699,e1700,e1701,e1702,e1703,e1704
,e1705,e1706,e1707,e1708,e1709,e1710,e1711,e1712,e1713,e1714,e1715
,e1716,e1717,e1718,e1719,e1720,e1721,e1722,e1723,e1724,e1725,e1726
,e1727,e1728,e1729,e1730,e1731,e1732,e1733,e1734,e1735,e1736,e1737
,e1738,e1739,e1740,e1741,e1742,e1743,e1744,e1745,e1746,e1747,e1748
,e1749,e1750,e1751,e1752,e1753,e1754,e1755,e1756,e1757,e1758,e1759
,e1760,e1761,e1762,e1763,e1764,e1765,e1766,e1767,e1768,e1769,e1770
,e1771,e1772,e1773,e1774,e1775,e1776,e1777,e1778,e1779,e1780,e1781
,e1782,e1783,e1784,e1785,e1786,e1787,e1788,e1789,e1790,e1791,e1792
,e1793,e1794,e1795,e1796,e1797,e1798,e1799,e1800,e1801,e1802,e1803
,e1804,e1805,e1806,e1807,e1808,e1809,e1810,e1811,e1812,e1813,e1814
,e1815,e1816,e1817,e1818,e1819,e1820,e1821,e1822,e1823,e1824,e1825
,e1826,e1827,e1828,e1829,e1830,e1831,e1832,e1833,e1834,e1835,e1836
,e1837,e1838,e1839,e1840,e1841,e1842,e1843,e1844,e1845,e1846,e1847
,e1848,e1849,e1850,e1851,e1852,e1853,e1854,e1855,e1856,e1857,e1858
,e1859,e1860,e1861,e1862,e1863,e1864,e1865,e1866,e1867,e1868,e1869
,e1870,e1871,e1872,e1873,e1874,e1875,e1876,e1877,e1878,e1879,e1880
,e1881,e1882,e1883,e1884,e1885,e1886,e1887,e1888,e1889,e1890,e1891
,e1892,e1893,e1894,e1895,e1896,e1897,e1898,e1899,e1900,e1901,e1902
,e1903,e1904,e1905,e1906,e1907,e1908,e1909,e1910,e1911,e1912,e1913
,e1914,e1915,e1916,e1917,e1918,e1919,e1920,e1921,e1922,e1923,e1924
,e1925,e1926,e1927,e1928,e1929,e1930,e1931,e1932,e1933,e1934,e1935
,e1936,e1937,e1938,e1939,e1940,e1941,e1942,e1943,e1944,e1945,e1946
,e1947,e1948,e1949,e1950,e1951,e1952,e1953,e1954,e1955,e1956,e1957
,e1958,e1959,e1960,e1961,e1962,e1963,e1964,e1965,e1966,e1967,e1968
,e1969,e1970,e1971,e1972,e1973,e1974,e1975,e1976,e1977,e1978,e1979
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