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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 ,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35 ,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52 ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69 ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86 ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102 ,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115 ,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128 ,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141 ,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154 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,x99819,x99820,x99821,x99822,x99823,x99824,x99825,x99826,x99827 ,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 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