MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance gtm
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 543.56509480 (ANTIGONE) 543.56509420 (BARON) 543.56508370 (COUENNE) 543.56509470 (LINDO) 543.56509310 (SCIP) |
| Referencesⓘ | Manne, Alan S and Beltramo, M A, GTM: An International Gas Trade Model, International Energy Program Report, Stanford University, 1984. |
| Sourceⓘ | GAMS Model Library model gtm |
| Applicationⓘ | Gas Trade |
| Added to libraryⓘ | 31 Jul 2001 |
| Removed from libraryⓘ | 16 Feb 2022 |
| Removed becauseⓘ | Instance is continuous and convex. |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 63 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 20 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 59 |
| #Nonlinear Nonzeros in Objectiveⓘ | 20 |
| #Constraintsⓘ | 24 |
| #Linear Constraintsⓘ | 24 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div log vcpower |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 102 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 20 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 20 |
| #Blocks in Hessian of Lagrangianⓘ | 20 |
| 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ⓘ | 3.7200e-02 |
| Maximal coefficientⓘ | 3.2561e+02 |
| Infeasibility of initial pointⓘ | 2.2 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 25 1 14 10 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 64 64 0 0 0 0 0 0
* FX 4
*
* Nonzero counts
* Total const NL DLL
* 162 142 20 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,objvar;
Positive 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;
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;
e1.. x1 + x2 + x3 + x4 + x5 + x6 - x40 =L= 0;
e2.. x7 + x8 + x9 + x10 + x11 + x12 + x13 + x14 + x15 + x16 - x41 =L= 0;
e3.. x17 + x18 - x42 =L= 0;
e4.. x19 + x20 - x43 =L= 0;
e5.. x21 + x22 + x23 + x24 + x25 + x26 - x44 =L= 0;
e6.. x27 + x28 + x29 - x45 =L= 0;
e7.. x30 + x31 + x32 - x46 =L= 0;
e8.. x33 + x34 + x35 + x36 + x37 - x47 =L= 0;
e9.. x38 - x48 =L= 0;
e10.. x39 - x49 =L= 0;
e11.. x1 - x50 =G= 0;
e12.. x17 - x51 =G= 0;
e13.. x7 - x52 =G= 0;
e14.. x8 - x53 =G= 0;
e15.. x9 + x18 + x21 - x54 =G= 0;
e16.. x2 + x10 + x22 - x55 =G= 0;
e17.. x3 + x11 + x19 + x23 - x56 =G= 0;
e18.. x4 + x24 - x57 =G= 0;
e19.. x5 + x12 + x20 + x25 + x27 + x30 + x33 + x39 - x58 =G= 0;
e20.. x26 + x28 + x31 - x59 =G= 0;
e21.. x13 + x29 + x34 - x60 =G= 0;
e22.. x14 + x35 - x61 =G= 0;
e23.. x6 + x15 + x32 + x36 + x38 - x62 =G= 0;
e24.. x16 + x37 - x63 =G= 0;
e25.. -(-4.84/x50 - 0.14/x51 - 6.4827/x52 - 6.6654/x53 - 8.89583741831423*x54**
(-0.666666666666667) - 20.7788808225955*x55**(-0.515151515151515) -
12.8222379289592*x56**(-0.538461538461538) - 112.274462577384*x57**(-
0.123595505617978) - 78.984522912416*x58**(-0.538461538461538) -
325.606233858943*x59**(-0.19047619047619) - 19.9925533406708*x60**(-
0.492537313432836) - 20.2959676146409*x61**(-0.851851851851852) -
34.6492709112034*x62**(-1.32558139534884) - 2.07326743881507*x63**(-
0.754385964912281) - (0.0372*x44 - 6.47537234042553*log(1 -
0.102564102564103*x44) - 0.489999999999999*log(1 - 1.38888888888889*x43)
- 1.68*log(1 - 0.392156862745098*x45) - 1.2271875*log(1 -
0.581395348837209*x46) - 0.2187*x46 - 0.979999999999999*log(1 -
0.694444444444444*x47) - 0.35*log(1 - 1.92307692307692*x48))) + 0.25*x1
+ 2.29*x2 + 2.22*x3 + 2.03*x4 + 1.96*x5 + 2.13*x6 + 0.4*x7 + 0.9*x8
+ 1.15*x9 + 1.1*x10 + 1.1*x11 + 0.8*x12 + 0.8*x13 + 0.65*x14 + 0.7*x15
+ 0.65*x16 + 1.5*x18 + 0.72*x19 + 0.46*x20 + 2.12*x21 + 1.08*x22
+ 1.01*x23 + 0.82*x24 + 0.75*x25 + 0.04*x26 + 0.86*x27 + 0.14*x28
+ 0.64*x29 + 0.77*x30 + 0.05*x31 + 0.94*x32 + 0.53*x33 + 0.31*x34
+ 0.58*x35 + 0.7*x36 + 1.91*x37 + 0.43*x38 + 6*x39 + 2*x49 - objvar
=E= 0;
* set non-default bounds
x2.up = 0.067;
x3.up = 0.067;
x4.up = 0.067;
x5.up = 0.067;
x6.up = 0.033;
x9.up = 0.3;
x10.up = 0.15;
x11.up = 0.1;
x19.up = 0.34;
x20.up = 0.35;
x22.up = 1.39;
x23.up = 1.06;
x24.up = 2;
x25.up = 2.62;
x26.up = 3.73;
x27.up = 0.62;
x28.up = 2.3;
x29.up = 1.03;
x30.up = 0.12;
x31.up = 1.45;
x32.up = 1.46;
x33.up = 0.48;
x34.up = 0.14;
x36.up = 0.1;
x38.up = 0.48;
x39.up = 0.8;
x40.up = 2.475;
x41.up = 3.7125;
x42.up = 0.297;
x43.up = 0.7128;
x44.up = 9.6525;
x45.up = 2.5245;
x46.up = 1.7028;
x47.up = 1.4256;
x48.up = 0.5148;
x49.up = 99;
x50.fx = 2.2;
x51.fx = 0.2;
x52.fx = 1.47;
x53.fx = 1.38;
x54.lo = 0.2;
x55.lo = 0.2;
x56.lo = 0.2;
x57.lo = 0.2;
x58.lo = 0.2;
x59.lo = 0.2;
x60.lo = 0.2;
x61.lo = 0.2;
x62.lo = 0.2;
x63.lo = 0.2;
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