MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance otpop
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -0.00000051 (ANTIGONE) -0.00000000 (BARON) -0.00000000 (COUENNE) 0.00000000 (LINDO) -0.00000000 (SCIP) |
| Referencesⓘ | Blitzer, C, Meeraus, Alexander, and Stoutjesdijk, Ardy J, A Dynamic model of OPEC Trade and Production, Journal of Development Economics, 2:4, 1975, 319-335. |
| Sourceⓘ | GAMS Model Library model otpop |
| Applicationⓘ | Production |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 103 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 66 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 17 |
| #Nonlinear Nonzeros in Objectiveⓘ | 17 |
| #Constraintsⓘ | 76 |
| #Linear Constraintsⓘ | 43 |
| #Quadratic Constraintsⓘ | 16 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 17 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 250 |
| #Nonlinear Nonzeros in Jacobianⓘ | 66 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 83 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 17 |
| #Blocks in Hessian of Lagrangianⓘ | 33 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 4.2960e-03 |
| Maximal coefficientⓘ | 1.3728e+01 |
| Infeasibility of initial pointⓘ | 165.2 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 77 77 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 104 104 0 0 0 0 0 0
* FX 11
*
* Nonzero counts
* Total const NL DLL
* 268 185 83 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
,objvar;
Positive Variables x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17;
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;
e1.. x18 =E= 88.2;
e2.. x19 =E= 91.728;
e3.. x20 =E= 95.39712;
e4.. x21 =E= 99.2130048;
e5.. x22 =E= 103.181524992;
e6.. x23 =E= 107.30878599168;
e7.. x24 =E= 111.601137431347;
e8.. x25 =E= 116.065182928601;
e9.. x26 =E= 120.707790245745;
e10.. x27 =E= 125.536101855575;
e11.. x28 =E= 130.557545929798;
e12.. x29 =E= 135.77984776699;
e13.. x30 =E= 141.21104167767;
e14.. x31 =E= 146.859483344776;
e15.. x32 =E= 152.733862678567;
e16.. x33 =E= 158.84321718571;
e17.. x34 =E= 165.196945873138;
e18.. x61**0.2*x35 + x1 - x18 =E= 0;
e19.. x62**0.2*x36 + x2 - x19 =E= 0;
e20.. x63**0.2*x37 + x3 - x20 =E= 0;
e21.. x64**0.2*x38 + x4 - x21 =E= 0;
e22.. x65**0.2*x39 + x5 - x22 =E= 0;
e23.. x66**0.2*x40 + x6 - x23 =E= 0;
e24.. x67**0.2*x41 + x7 - x24 =E= 0;
e25.. x68**0.2*x42 + x8 - x25 =E= 0;
e26.. x69**0.2*x43 + x9 - x26 =E= 0;
e27.. x70**0.2*x44 + x10 - x27 =E= 0;
e28.. x71**0.2*x45 + x11 - x28 =E= 0;
e29.. x72**0.2*x46 + x12 - x29 =E= 0;
e30.. x73**0.2*x47 + x13 - x30 =E= 0;
e31.. x74**0.2*x48 + x14 - x31 =E= 0;
e32.. x75**0.2*x49 + x15 - x32 =E= 0;
e33.. x76**0.2*x50 + x16 - x33 =E= 0;
e34.. x77**0.2*x51 + x17 - x34 =E= 0;
e35.. -0.00429596009984836*x18*(-3 + x84) - x35 + x36 =E= 0;
e36.. -0.00429596009984836*x19*(-3 + x85) - x36 + x37 =E= 0;
e37.. -0.00429596009984836*x20*(-3 + x86) - x37 + x38 =E= 0;
e38.. -0.00429596009984836*x21*(-3 + x87) - x38 + x39 =E= 0;
e39.. -0.00429596009984836*x22*(-3 + x88) - x39 + x40 =E= 0;
e40.. -0.00429596009984836*x23*(-3 + x89) - x40 + x41 =E= 0;
e41.. -0.00429596009984836*x24*(-3 + x90) - x41 + x42 =E= 0;
e42.. -0.00429596009984836*x25*(-3 + x91) - x42 + x43 =E= 0;
e43.. -0.00429596009984836*x26*(-3 + x92) - x43 + x44 =E= 0;
e44.. -0.00429596009984836*x27*(-3 + x93) - x44 + x45 =E= 0;
e45.. -0.00429596009984836*x28*(-3 + x94) - x45 + x46 =E= 0;
e46.. -0.00429596009984836*x29*(-3 + x95) - x46 + x47 =E= 0;
e47.. -0.00429596009984836*x30*(-3 + x96) - x47 + x48 =E= 0;
e48.. -0.00429596009984836*x31*(-3 + x97) - x48 + x49 =E= 0;
e49.. -0.00429596009984836*x32*(-3 + x98) - x49 + x50 =E= 0;
e50.. -0.00429596009984836*x33*(-3 + x99) - x50 + x51 =E= 0;
e51.. - 0.5*x52 + x78 =E= 0;
e52.. - 0.3*x52 - 0.5*x53 + x79 =E= 0;
e53.. - 0.2*x52 - 0.3*x53 - 0.5*x54 + x80 =E= 0;
e54.. - 0.2*x53 - 0.3*x54 - 0.5*x55 + x81 =E= 0;
e55.. - 0.2*x54 - 0.3*x55 - 0.5*x56 + x82 =E= 0;
e56.. - 0.2*x55 - 0.3*x56 - 0.5*x57 + x83 =E= 0;
e57.. - 0.2*x56 - 0.3*x57 - 0.5*x58 + x84 =E= 0;
e58.. - 0.2*x57 - 0.3*x58 - 0.5*x59 + x85 =E= 0;
e59.. - 0.2*x58 - 0.3*x59 - 0.5*x60 + x86 =E= 0;
e60.. - 0.2*x59 - 0.3*x60 - 0.5*x61 + x87 =E= 0;
e61.. - 0.2*x60 - 0.3*x61 - 0.5*x62 + x88 =E= 0;
e62.. - 0.2*x61 - 0.3*x62 - 0.5*x63 + x89 =E= 0;
e63.. - 0.2*x62 - 0.3*x63 - 0.5*x64 + x90 =E= 0;
e64.. - 0.2*x63 - 0.3*x64 - 0.5*x65 + x91 =E= 0;
e65.. - 0.2*x64 - 0.3*x65 - 0.5*x66 + x92 =E= 0;
e66.. - 0.2*x65 - 0.3*x66 - 0.5*x67 + x93 =E= 0;
e67.. - 0.2*x66 - 0.3*x67 - 0.5*x68 + x94 =E= 0;
e68.. - 0.2*x67 - 0.3*x68 - 0.5*x69 + x95 =E= 0;
e69.. - 0.2*x68 - 0.3*x69 - 0.5*x70 + x96 =E= 0;
e70.. - 0.2*x69 - 0.3*x70 - 0.5*x71 + x97 =E= 0;
e71.. - 0.2*x70 - 0.3*x71 - 0.5*x72 + x98 =E= 0;
e72.. - 0.2*x71 - 0.3*x72 - 0.5*x73 + x99 =E= 0;
e73.. - 0.2*x72 - 0.3*x73 - 0.5*x74 + x100 =E= 0;
e74.. - 0.2*x73 - 0.3*x74 - 0.5*x75 + x101 =E= 0;
e75.. - 0.2*x74 - 0.3*x75 - 0.5*x76 + x102 =E= 0;
e76.. - 0.2*x75 - 0.3*x76 - 0.5*x77 + x103 =E= 0;
e77.. -(sqr(10 - x61) + sqr(10.2 - x62) + sqr(10.404 - x63) + sqr(10.61208 -
x64) + sqr(10.8243216 - x65) + sqr(11.040808032 - x66) + sqr(
11.26162419264 - x67) + sqr(11.4868566764928 - x68) + sqr(
11.7165938100227 - x69) + sqr(11.9509256862231 - x70) + sqr(
12.1899441999476 - x71) + sqr(12.4337430839465 - x72) + sqr(
12.6824179456255 - x73) + sqr(12.936066304538 - x74) + sqr(
13.1947876306287 - x75) + sqr(13.4586833832413 - x76) + sqr(
13.7278570509061 - x77)) + objvar =E= 0;
* set non-default bounds
x1.fx = 29.4;
x2.up = 35.25;
x3.up = 38.25;
x4.up = 41.25;
x5.up = 44.25;
x6.up = 47.25;
x7.up = 50.25;
x8.up = 51.15;
x9.up = 52.05;
x10.up = 52.95;
x11.up = 53.85;
x12.up = 54.75;
x13.up = 55.65;
x14.up = 56.55;
x15.up = 57.45;
x16.up = 58.35;
x17.up = 59.25;
x52.fx = 3.5;
x53.fx = 3.5;
x54.fx = 3.5;
x55.fx = 3.5;
x56.fx = 3.5;
x57.fx = 3.5;
x58.fx = 3.5;
x59.fx = 4;
x60.fx = 7;
x61.fx = 10;
x62.lo = 1;
x63.lo = 1;
x64.lo = 1;
x65.lo = 1;
x66.lo = 1;
x67.lo = 1;
x68.lo = 1;
x69.lo = 1;
x70.lo = 1;
x71.lo = 1;
x72.lo = 1;
x73.lo = 1;
x74.lo = 1;
x75.lo = 1;
x76.lo = 1;
x77.lo = 1;
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: 2024-08-26 Git hash: 6cc1607f