MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance chenery
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1177.80785100 (ANTIGONE) -1058.91986300 (BARON) -1058.91987100 (COUENNE) -1098.23486700 (LINDO) -1058.91985900 (SCIP) |
| Referencesⓘ | Chenery, Hollis B and Raduchel, W J, Substitution and Structural Change. In Chenery, Hollis B, Ed, Structural Change and Development Policy, Oxford University Press, New York and Oxford, 1981. |
| Sourceⓘ | GAMS Model Library model chenery |
| Applicationⓘ | Production |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 43 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 35 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 4 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 38 |
| #Linear Constraintsⓘ | 15 |
| #Quadratic Constraintsⓘ | 7 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 8 |
| #General Nonlinear Constraintsⓘ | 8 |
| Operands in Gen. Nonlin. Functionsⓘ | div vcpower |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 128 |
| #Nonlinear Nonzeros in Jacobianⓘ | 56 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 54 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 10 |
| #Blocks in Hessian of Lagrangianⓘ | 13 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 13 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.692308 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| Maximal coefficientⓘ | 4.5000e+02 |
| Infeasibility of initial pointⓘ | 217 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 39 33 4 2 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 44 44 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 133 77 56 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,objvar,x41,x42,x43,x44;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x17,x18,x19,x20,x21
,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
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;
e1.. - x9 - x10 - x11 - x12 - objvar =E= 0;
e2.. x1 - x9 - x25 + x28 =G= 0;
e3.. - 0.1*x1 + x2 - x10 - x26 + x29 =G= 0;
e4.. - 0.2*x1 - 0.1*x2 + x3 - x11 - x27 + x30 =G= 0;
e5.. - 0.2*x1 - 0.3*x2 - 0.1*x3 + x4 - x12 =G= 0;
e6.. x31*x28 - x34*x25 + x32*x29 - x35*x26 + x33*x30 - x36*x27 =L= 0;
e7.. - 0.005*x28 + x31 =E= 1;
e8.. - 0.0157*x29 + x32 =E= 1;
e9.. - 0.00178*x30 + x33 =E= 1;
e10.. 0.005*x25 + x34 =E= 1;
e11.. 0.001*x26 + x35 =E= 1.1;
e12.. 0.01*x27 + x36 =E= 1;
e13.. -100*(x39*x13)**(-0.674) + x9 =E= 0;
e14.. -230*(x39*x14)**(-0.246) + x10 =E= 0;
e15.. -220*(x39*x15)**(-0.587) + x11 =E= 0;
e16.. -450*(x39*x16)**(-0.352) + x12 =E= 0;
e17.. x17*x1 + x18*x2 + x19*x3 + x20*x4 =L= 750;
e18.. x21*x1 + x22*x2 + x23*x3 + x24*x4 =E= 500;
e19.. - x5 + x13 - 0.1*x14 - 0.2*x15 - 0.2*x16 =E= 0;
e20.. - x6 + x14 - 0.1*x15 - 0.3*x16 =E= 0;
e21.. - x7 + x15 - 0.1*x16 =E= 0;
e22.. - x8 + x16 =E= 0;
e23.. - x37 + x38 =E= 0;
e24.. -(2.06748466257669*x38)**(-0.89) + x41 =E= 0;
e25.. -(1.25733634311512*x38)**(-0.71) + x42 =E= 0;
e26.. -(0.00908173562058528*x38)**(-0.8) + x43 =E= 0;
e27.. -(124.31328320802*x38)**(-0.95) + x44 =E= 0;
e28.. -(0.674 + 0.326/x41)**0.123595505617978 + 3.97*x17 =E= 0;
e29.. -(0.557 + 0.443/x42)**0.408450704225352 + 3.33*x18 =E= 0;
e30.. -(0.00900000000000001 + 0.991/x43)**0.25 + 1.67*x19 =E= 0;
e31.. -(0.99202 + 0.00798/x44)**0.0526315789473684 + 1.84*x20 =E= 0;
e32.. -(0.326 + 0.674*x41)**0.123595505617978 + 3.97*x21 =E= 0;
e33.. -(0.443 + 0.557*x42)**0.408450704225352 + 3.33*x22 =E= 0;
e34.. -(0.991 + 0.00900000000000001*x43)**0.25 + 1.67*x23 =E= 0;
e35.. -(0.00798 + 0.99202*x44)**0.0526315789473684 + 1.84*x24 =E= 0;
e36.. -x37*x21 + x5 - x17 =E= 0;
e37.. -x37*x22 + x6 - x18 =E= 0;
e38.. -x37*x23 + x7 - x19 =E= 0;
e39.. -x37*x24 + x8 - x20 =E= 0;
* set non-default bounds
x1.up = 2000;
x2.up = 2000;
x3.up = 2000;
x4.up = 2000;
x5.up = 100;
x6.up = 100;
x7.up = 100;
x8.up = 100;
x9.up = 2000;
x10.up = 2000;
x11.up = 2000;
x12.up = 2000;
x13.lo = 0.1; x13.up = 100;
x14.lo = 0.1; x14.up = 100;
x15.lo = 0.1; x15.up = 100;
x16.lo = 0.1; x16.up = 100;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 400;
x26.up = 400;
x27.up = 400;
x28.up = 400;
x29.up = 400;
x30.up = 400;
x31.up = 4;
x32.up = 4;
x33.up = 4;
x34.up = 4;
x35.up = 4;
x36.up = 4;
x37.lo = 0.25; x37.up = 4;
x38.lo = 0.25; x38.up = 4;
x39.lo = 0.01;
x41.lo = 0.001;
x42.lo = 0.001;
x43.lo = 0.001;
x44.lo = 0.001;
* set non-default levels
x1.l = 200;
x2.l = 200;
x3.l = 200;
x4.l = 200;
x5.l = 1.08002386572984;
x6.l = 1.25850763714561;
x7.l = 2.47224270643972;
x8.l = 2.08174548233022;
x9.l = 250;
x10.l = 250;
x11.l = 250;
x12.l = 250;
x13.l = 3;
x14.l = 3;
x15.l = 3;
x16.l = 3;
x17.l = 0.283078383128534;
x18.l = 0.383990781960791;
x19.l = 0.309951359679435;
x20.l = 0.580992426342466;
x21.l = 0.22769870931466;
x22.l = 0.249861958624235;
x23.l = 0.617797527645794;
x24.l = 0.428786587425074;
x31.l = 1;
x32.l = 1;
x33.l = 1;
x34.l = 1;
x35.l = 1.1;
x36.l = 1;
x37.l = 3.5;
x38.l = 3.5;
x39.l = 0.3;
x41.l = 0.171804999139287;
x42.l = 0.349221638418406;
x43.l = 15.7837604335036;
x44.l = 0.00311417990544524;
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