MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance pindyck
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -15462.80394000 (ANTIGONE) -2622.75137300 (BARON) -1911.71985800 (COUENNE) -1722.94454000 (GUROBI) -1889.88836700 (LINDO) -1437.94113400 (SCIP) |
| Referencesⓘ | Pindyck, R S, Gains to Producers from the Cartelization of Exhaustible Resources, The Review of Economics and Statistics, 60:2, 1978, 238-251. |
| Sourceⓘ | GAMS Model Library model pindyck |
| Applicationⓘ | Production |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 116 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 64 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 16 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 96 |
| #Linear Constraintsⓘ | 64 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 16 |
| #General Nonlinear Constraintsⓘ | 16 |
| Operands in Gen. Nonlin. Functionsⓘ | cvpower mul |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 320 |
| #Nonlinear Nonzeros in Jacobianⓘ | 80 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 128 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 32 |
| #Blocks in Hessian of Lagrangianⓘ | 16 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 4 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 4 |
| Average blocksize in Hessian of Lagrangianⓘ | 4.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 2.5000e+02 |
| Infeasibility of initial pointⓘ | 148.4 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 97 97 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 117 117 0 0 0 0 0 0
* FX 4
*
* Nonzero counts
* Total const NL DLL
* 337 257 80 0
*
* Solve m using NLP minimizing objvar;
Variables x1,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
,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x18
,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,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,x85,x86,x87,x88,x89
,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100;
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;
e1.. 0.13*x1 - 0.87*x17 + x18 =E= 3.3;
e2.. 0.13*x2 - 0.87*x18 + x19 =E= 3.3345;
e3.. 0.13*x3 - 0.87*x19 + x20 =E= 3.3695175;
e4.. 0.13*x4 - 0.87*x20 + x21 =E= 3.4050602625;
e5.. 0.13*x5 - 0.87*x21 + x22 =E= 3.4411361664375;
e6.. 0.13*x6 - 0.87*x22 + x23 =E= 3.47775320893406;
e7.. 0.13*x7 - 0.87*x23 + x24 =E= 3.51491950706807;
e8.. 0.13*x8 - 0.87*x24 + x25 =E= 3.55264329967409;
e9.. 0.13*x9 - 0.87*x25 + x26 =E= 3.5909329491692;
e10.. 0.13*x10 - 0.87*x26 + x27 =E= 3.62979694340674;
e11.. 0.13*x11 - 0.87*x27 + x28 =E= 3.66924389755784;
e12.. 0.13*x12 - 0.87*x28 + x29 =E= 3.70928255602121;
e13.. 0.13*x13 - 0.87*x29 + x30 =E= 3.74992179436153;
e14.. 0.13*x14 - 0.87*x30 + x31 =E= 3.79117062127695;
e15.. 0.13*x15 - 0.87*x31 + x32 =E= 3.8330381805961;
e16.. 0.13*x16 - 0.87*x32 + x33 =E= 3.87553375330505;
e17.. -1.02**(-0.142857142857143*x52)*(1.1 + 0.1*x1) - 0.75*x34 + x35 =E= 0;
e18.. -1.02**(-0.142857142857143*x53)*(1.1 + 0.1*x2) - 0.75*x35 + x36 =E= 0;
e19.. -1.02**(-0.142857142857143*x54)*(1.1 + 0.1*x3) - 0.75*x36 + x37 =E= 0;
e20.. -1.02**(-0.142857142857143*x55)*(1.1 + 0.1*x4) - 0.75*x37 + x38 =E= 0;
e21.. -1.02**(-0.142857142857143*x56)*(1.1 + 0.1*x5) - 0.75*x38 + x39 =E= 0;
e22.. -1.02**(-0.142857142857143*x57)*(1.1 + 0.1*x6) - 0.75*x39 + x40 =E= 0;
e23.. -1.02**(-0.142857142857143*x58)*(1.1 + 0.1*x7) - 0.75*x40 + x41 =E= 0;
e24.. -1.02**(-0.142857142857143*x59)*(1.1 + 0.1*x8) - 0.75*x41 + x42 =E= 0;
e25.. -1.02**(-0.142857142857143*x60)*(1.1 + 0.1*x9) - 0.75*x42 + x43 =E= 0;
e26.. -1.02**(-0.142857142857143*x61)*(1.1 + 0.1*x10) - 0.75*x43 + x44 =E= 0;
e27.. -1.02**(-0.142857142857143*x62)*(1.1 + 0.1*x11) - 0.75*x44 + x45 =E= 0;
e28.. -1.02**(-0.142857142857143*x63)*(1.1 + 0.1*x12) - 0.75*x45 + x46 =E= 0;
e29.. -1.02**(-0.142857142857143*x64)*(1.1 + 0.1*x13) - 0.75*x46 + x47 =E= 0;
e30.. -1.02**(-0.142857142857143*x65)*(1.1 + 0.1*x14) - 0.75*x47 + x48 =E= 0;
e31.. -1.02**(-0.142857142857143*x66)*(1.1 + 0.1*x15) - 0.75*x48 + x49 =E= 0;
e32.. -1.02**(-0.142857142857143*x67)*(1.1 + 0.1*x16) - 0.75*x49 + x50 =E= 0;
e33.. - x35 - x51 + x52 =E= 0;
e34.. - x36 - x52 + x53 =E= 0;
e35.. - x37 - x53 + x54 =E= 0;
e36.. - x38 - x54 + x55 =E= 0;
e37.. - x39 - x55 + x56 =E= 0;
e38.. - x40 - x56 + x57 =E= 0;
e39.. - x41 - x57 + x58 =E= 0;
e40.. - x42 - x58 + x59 =E= 0;
e41.. - x43 - x59 + x60 =E= 0;
e42.. - x44 - x60 + x61 =E= 0;
e43.. - x45 - x61 + x62 =E= 0;
e44.. - x46 - x62 + x63 =E= 0;
e45.. - x47 - x63 + x64 =E= 0;
e46.. - x48 - x64 + x65 =E= 0;
e47.. - x49 - x65 + x66 =E= 0;
e48.. - x50 - x66 + x67 =E= 0;
e49.. - x18 + x35 + x68 =E= 0;
e50.. - x19 + x36 + x69 =E= 0;
e51.. - x20 + x37 + x70 =E= 0;
e52.. - x21 + x38 + x71 =E= 0;
e53.. - x22 + x39 + x72 =E= 0;
e54.. - x23 + x40 + x73 =E= 0;
e55.. - x24 + x41 + x74 =E= 0;
e56.. - x25 + x42 + x75 =E= 0;
e57.. - x26 + x43 + x76 =E= 0;
e58.. - x27 + x44 + x77 =E= 0;
e59.. - x28 + x45 + x78 =E= 0;
e60.. - x29 + x46 + x79 =E= 0;
e61.. - x30 + x47 + x80 =E= 0;
e62.. - x31 + x48 + x81 =E= 0;
e63.. - x32 + x49 + x82 =E= 0;
e64.. - x33 + x50 + x83 =E= 0;
e65.. x68 - x84 + x85 =E= 0;
e66.. x69 - x85 + x86 =E= 0;
e67.. x70 - x86 + x87 =E= 0;
e68.. x71 - x87 + x88 =E= 0;
e69.. x72 - x88 + x89 =E= 0;
e70.. x73 - x89 + x90 =E= 0;
e71.. x74 - x90 + x91 =E= 0;
e72.. x75 - x91 + x92 =E= 0;
e73.. x76 - x92 + x93 =E= 0;
e74.. x77 - x93 + x94 =E= 0;
e75.. x78 - x94 + x95 =E= 0;
e76.. x79 - x95 + x96 =E= 0;
e77.. x80 - x96 + x97 =E= 0;
e78.. x81 - x97 + x98 =E= 0;
e79.. x82 - x98 + x99 =E= 0;
e80.. x83 - x99 + x100 =E= 0;
e81.. -(x1 - 250/x85)*x68 + x101 =E= 0;
e82.. -(x2 - 250/x86)*x69 + x102 =E= 0;
e83.. -(x3 - 250/x87)*x70 + x103 =E= 0;
e84.. -(x4 - 250/x88)*x71 + x104 =E= 0;
e85.. -(x5 - 250/x89)*x72 + x105 =E= 0;
e86.. -(x6 - 250/x90)*x73 + x106 =E= 0;
e87.. -(x7 - 250/x91)*x74 + x107 =E= 0;
e88.. -(x8 - 250/x92)*x75 + x108 =E= 0;
e89.. -(x9 - 250/x93)*x76 + x109 =E= 0;
e90.. -(x10 - 250/x94)*x77 + x110 =E= 0;
e91.. -(x11 - 250/x95)*x78 + x111 =E= 0;
e92.. -(x12 - 250/x96)*x79 + x112 =E= 0;
e93.. -(x13 - 250/x97)*x80 + x113 =E= 0;
e94.. -(x14 - 250/x98)*x81 + x114 =E= 0;
e95.. -(x15 - 250/x99)*x82 + x115 =E= 0;
e96.. -(x16 - 250/x100)*x83 + x116 =E= 0;
e97.. - x101 - 0.952380952380952*x102 - 0.90702947845805*x103
- 0.863837598531476*x104 - 0.822702474791882*x105
- 0.783526166468459*x106 - 0.746215396636628*x107
- 0.710681330130121*x108 - 0.676839362028687*x109
- 0.644608916217797*x110 - 0.613913253540759*x111
- 0.584679289086437*x112 - 0.556837418177559*x113
- 0.530321350645295*x114 - 0.505067952995519*x115
- 0.48101709809097*x116 - objvar =E= 0;
* set non-default bounds
x17.fx = 18;
x34.fx = 6.5;
x51.fx = 0;
x84.fx = 500;
* set non-default levels
x1.l = 14;
x2.l = 14;
x3.l = 14;
x4.l = 14;
x5.l = 14;
x6.l = 14;
x7.l = 14;
x8.l = 14;
x9.l = 14;
x10.l = 14;
x11.l = 14;
x12.l = 14;
x13.l = 14;
x14.l = 14;
x15.l = 14;
x16.l = 14;
x18.l = 18;
x19.l = 18;
x20.l = 18;
x21.l = 18;
x22.l = 18;
x23.l = 18;
x24.l = 18;
x25.l = 18;
x26.l = 18;
x27.l = 18;
x28.l = 18;
x29.l = 18;
x30.l = 18;
x31.l = 18;
x32.l = 18;
x33.l = 18;
x35.l = 7;
x36.l = 7;
x37.l = 7;
x38.l = 7;
x39.l = 7;
x40.l = 7;
x41.l = 7;
x42.l = 7;
x43.l = 7;
x44.l = 7;
x45.l = 7;
x46.l = 7;
x47.l = 7;
x48.l = 7;
x49.l = 7;
x50.l = 7;
x52.l = 7;
x53.l = 14;
x54.l = 21;
x55.l = 28;
x56.l = 35;
x57.l = 42;
x58.l = 49;
x59.l = 56;
x60.l = 63;
x61.l = 70;
x62.l = 77;
x63.l = 84;
x64.l = 91;
x65.l = 98;
x66.l = 105;
x67.l = 112;
x68.l = 11;
x69.l = 11;
x70.l = 11;
x71.l = 11;
x72.l = 11;
x73.l = 11;
x74.l = 11;
x75.l = 11;
x76.l = 11;
x77.l = 11;
x78.l = 11;
x79.l = 11;
x80.l = 11;
x81.l = 11;
x82.l = 11;
x83.l = 11;
x85.l = 489;
x86.l = 478;
x87.l = 467;
x88.l = 456;
x89.l = 445;
x90.l = 434;
x91.l = 423;
x92.l = 412;
x93.l = 401;
x94.l = 390;
x95.l = 379;
x96.l = 368;
x97.l = 357;
x98.l = 346;
x99.l = 335;
x100.l = 324;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc