MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance demo7
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1589042.38800000 (BARON) -1589042.38600000 (COUENNE) -1589042.38600000 (LINDO) -1589042.38600000 (SCIP) |
| Referencesⓘ | Kutcher, Gary P, Meeraus, Alexander, and O'Mara, Gerald T, Agriculture Sector and Policy Models, The World Bank, 1988. |
| Sourceⓘ | GAMS Model Library model demo7 |
| Applicationⓘ | Agriculture |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | QCQP |
| #Variablesⓘ | 70 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 6 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 13 |
| #Nonlinear Nonzeros in Objectiveⓘ | 6 |
| #Constraintsⓘ | 57 |
| #Linear Constraintsⓘ | 56 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 281 |
| #Nonlinear Nonzeros in Jacobianⓘ | 6 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 6 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| 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ⓘ | 6.6667e-03 |
| Maximal coefficientⓘ | 7.0000e+02 |
| Infeasibility of initial pointⓘ | 500 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 58 30 2 26 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 71 71 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 295 283 12 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,objvar,x69
,x70,x71;
Positive Variables x1,x2,x3,x4,x5,x6,x7,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,x62,x63
,x64,x65,x66,x67;
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;
e1.. x1 + x2 + x3 + x4 =L= 4000;
e2.. x1 + x2 + x3 + x4 =L= 4000;
e3.. x1 + 0.5*x2 + x3 + x4 + 0.5*x5 =L= 4000;
e4.. x1 + x3 + x4 + x5 =L= 4000;
e5.. x1 + 0.25*x4 + x5 + 0.25*x6 =L= 4000;
e6.. x5 + x6 =L= 4000;
e7.. x5 + x6 + 0.75*x7 =L= 4000;
e8.. x5 + x6 + x7 =L= 4000;
e9.. x5 + x6 + x7 =L= 4000;
e10.. x5 + 0.5*x6 + x7 =L= 4000;
e11.. 0.5*x1 + 0.25*x2 + 0.25*x3 + 0.5*x4 + 0.75*x5 + 0.75*x7 =L= 4000;
e12.. x1 + x2 + x3 + x4 =L= 4000;
e13.. 1.72*x1 + 4.5*x2 + 0.75*x3 + 5.16*x4 - x15 - x27 + 2*x39 + 2*x40 =L= 0
;
e14.. 0.5*x1 + x2 + 0.75*x3 + 5*x4 - x16 - x28 + 2*x39 + 2*x40 =L= 0;
e15.. x1 + 8*x2 + 0.75*x3 + 5*x4 + 5*x5 - x17 - x29 + 2*x39 + 2*x40 =L= 0;
e16.. x1 + 16*x3 + 19.58*x4 + 5*x5 - x18 - x30 + 2*x39 + 2*x40 =L= 0;
e17.. 17.16*x1 + 2.42*x4 + 9*x5 + 4.3*x6 - x19 - x31 + 2*x39 + 2*x40 =L= 0;
e18.. 2.34*x1 + 2*x5 + 5.04*x6 - x20 - x32 + 2*x39 + 2*x40 =L= 0;
e19.. 1.5*x5 + 7.16*x6 + 17*x7 - x21 - x33 + 2*x39 + 2*x40 =L= 0;
e20.. 2*x5 + 7.97*x6 + 15*x7 - x22 - x34 + 2*x39 + 2*x40 =L= 0;
e21.. x5 + 4.41*x6 + 12*x7 - x23 - x35 + 2*x39 + 2*x40 =L= 0;
e22.. 26*x5 + 1.12*x6 + 7*x7 - x24 - x36 + 2*x39 + 2*x40 =L= 0;
e23.. 2.43*x1 + 2.5*x2 + 7.5*x3 + 11.16*x4 + 12*x5 + 6*x7 - x25 - x37
+ 2*x39 + 2*x40 =L= 0;
e24.. 1.35*x1 + 7.5*x2 + 0.75*x3 + 4.68*x4 - x26 - x38 + 2*x39 + 2*x40 =L= 0
;
e25.. x5 + x6 + x7 - 2*x39 - 2*x40 - x48 =L= 0;
e26.. x1 + x2 + x3 + x4 - 2*x39 - 2*x40 - x49 =L= 0;
e27.. x13 - 3*x15 - 3*x16 - 3*x17 - 3*x18 - 3*x19 - 3*x20 - 3*x21 - 3*x22
- 3*x23 - 3*x24 - 3*x25 - 3*x26 =E= 0;
e28.. -(225*x50 - 0.0462962962962963*sqr(x50) - 0.555555555555555*sqr(x51) +
700*x51 - 0.178571428571429*sqr(x52) + 250*x52 - 0.166666666666667*sqr(
x53) + 700*x53 - 0.0368421052631579*sqr(x54) + 210*x54 - 0.2*sqr(x55) +
220*x55) + x9 - 40*x62 - 300*x63 - 60*x64 =E= 0;
e29.. x12 - 4*x27 - 4*x28 - 4*x29 - 4*x30 - 4*x31 - 4*x32 - 4*x33 - 4*x34
- 4*x35 - 4*x36 - 4*x37 - 4*x38 =E= 0;
e30.. - x10 - x11 - x12 - x13 + x14 =E= 0;
e31.. - x41 + x50 - x65 =E= 0;
e32.. - x43 + x51 - x66 =E= 0;
e33.. - x44 + x52 + x62 =E= 0;
e34.. - x45 + x53 + x63 =E= 0;
e35.. - x46 + x54 - x67 =E= 0;
e36.. - x47 + x55 + x64 =E= 0;
e37.. - 0.0916666666666667*x1 - 0.0783333333333333*x2 - 0.0883333333333333*x3
- 0.176666666666667*x4 - 0.211666666666667*x5 - 0.1*x6 - 0.19*x7
- 0.00666666666666667*x39 - 0.00666666666666667*x40 + x70 =E= 0;
e38.. - 1.5*x1 + x41 =E= 0;
e39.. - 6*x2 + x42 =E= 0;
e40.. - x3 + x43 =E= 0;
e41.. - 3*x4 + x44 =E= 0;
e42.. - 1.5*x5 + x45 =E= 0;
e43.. - 2*x6 + x46 =E= 0;
e44.. - 3*x7 + x47 =E= 0;
e45.. - 100*x41 - 200*x43 - 125*x44 - 350*x45 - 70*x46 - 120*x47 + x69 =E= 0;
e46.. - 10*x1 - 5*x3 - 50*x4 - 80*x5 - 5*x6 - 50*x7 + x10 =E= 0;
e47.. x11 - 40*x48 - 40*x49 =E= 0;
e48.. 6*x2 - 1.3*x39 - 2*x40 =G= 0;
e49.. 1.75*x1 - 1.6*x39 - 0.8*x40 =G= 0;
e50.. - x8 - x9 - x13 + x14 =E= 0;
e51.. - 40*x62 - 300*x63 - 60*x64 + 140*x65 + 270*x66 + 85*x67 + x71 =E= 0;
e52.. 0.0462962962962963*x50 + x56 =E= 225;
e53.. 0.555555555555555*x51 + x57 =E= 700;
e54.. 0.178571428571429*x52 + x58 =E= 250;
e55.. 0.166666666666667*x53 + x59 =E= 700;
e56.. 0.0368421052631579*x54 + x60 =E= 210;
e57.. 0.2*x55 + x61 =E= 220;
e58.. -(225*x50 - 0.0231481481481481*sqr(x50) - 0.277777777777778*sqr(x51) +
700*x51 - 0.0892857142857143*sqr(x52) + 250*x52 - 0.0833333333333333*sqr(
x53) + 700*x53 - 0.0184210526315789*sqr(x54) + 210*x54 - 0.1*sqr(x55) +
220*x55) + x14 - 40*x62 - 300*x63 - 60*x64 + 140*x65 + 270*x66 + 85*x67
- objvar =E= 0;
* set non-default bounds
x15.up = 25000;
x16.up = 25000;
x17.up = 25000;
x18.up = 25000;
x19.up = 25000;
x20.up = 25000;
x21.up = 25000;
x22.up = 25000;
x23.up = 25000;
x24.up = 25000;
x25.up = 25000;
x26.up = 25000;
* set non-default levels
x56.l = 100;
x57.l = 200;
x58.l = 125;
x59.l = 350;
x60.l = 70;
x61.l = 120;
* set non-default marginals
e17.m = 1;
e22.m = 1;
e27.m = 1;
e28.m = 1;
e29.m = 1;
e30.m = 1;
e31.m = 1;
e32.m = 1;
e33.m = 1;
e34.m = 1;
e35.m = 1;
e36.m = 1;
e37.m = 1;
e39.m = 1;
e40.m = 1;
e41.m = 1;
e43.m = 1;
e44.m = 1;
e45.m = 1;
e46.m = 1;
e47.m = 1;
e50.m = 1;
e51.m = 1;
e52.m = 1;
e53.m = 1;
e54.m = 1;
e55.m = 1;
e56.m = 1;
e57.m = 1;
x15.m = 1;
x16.m = 1;
x17.m = 1;
x18.m = 1;
x19.m = 1;
x20.m = 1;
x21.m = 1;
x22.m = 1;
x23.m = 1;
x24.m = 1;
x25.m = 1;
x26.m = 1;
x27.m = 1;
x28.m = 1;
x29.m = 1;
x30.m = 1;
x31.m = 1;
x32.m = 1;
x33.m = 1;
x34.m = 1;
x35.m = 1;
x36.m = 1;
x37.m = 1;
x38.m = 1;
x39.m = 1;
x40.m = 1;
x41.m = 1;
x42.m = 1;
x43.m = 1;
x44.m = 1;
x45.m = 1;
x46.m = 1;
x47.m = 1;
x48.m = 1;
x49.m = 1;
x50.m = 1;
x52.m = 1;
x53.m = 1;
x54.m = 1;
x55.m = 1;
x66.m = 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: 2025-08-07 Git hash: e62cedfc