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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance gsg_0001
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2335.69947600 (ANTIGONE) 2378.16050800 (BARON) 2378.16046000 (COUENNE) 2378.16051200 (LINDO) 2378.16049100 (SCIP) 0.00000000 (SHOT) |
| Sourceⓘ | GAMS Software GmbH Client Model |
| Added to libraryⓘ | 11 Dec 2003 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 78 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 44 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 112 |
| #Linear Constraintsⓘ | 111 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 1 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 369 |
| #Nonlinear Nonzeros in Jacobianⓘ | 44 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 66 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 22 |
| #Blocks in Hessian of Lagrangianⓘ | 22 |
| 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ⓘ | 7.6045e-03 |
| Maximal coefficientⓘ | 1.3000e+02 |
| Infeasibility of initial pointⓘ | 509.4 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 112 41 41 30 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 78 78 0 0 0 0 0 0
* FX 5
*
* Nonzero counts
* Total const NL DLL
* 369 325 44 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,objvar;
Positive Variables 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,x68
,x69,x70,x71,x72,x73,x74,x75,x76,x77;
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,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112;
e1.. x1 + x12 + x23 =G= 12.735;
e2.. x2 + x13 + x24 =G= 18.523;
e3.. x3 + x14 + x25 =G= 24.42;
e4.. x4 + x15 + x26 =G= 30.729;
e5.. x5 + x16 + x27 =G= 41.698;
e6.. x6 + x17 + x28 =G= 52.802;
e7.. x7 + x18 + x29 =G= 65.155;
e8.. x8 + x19 + x30 =G= 81.675;
e9.. x9 + x20 + x31 =G= 98.667;
e10.. x10 + x21 + x32 =G= 115.501;
e11.. x11 + x22 + x33 =G= 133.561;
e12.. - 0.744093914896725*x1 + x2 =G= 0;
e13.. - 0.744093914896725*x2 + x3 =G= 0;
e14.. - 0.744093914896725*x3 + x4 =G= 0;
e15.. - 0.744093914896725*x4 + x5 =G= 0;
e16.. - 0.744093914896725*x5 + x6 =G= 0;
e17.. - 0.744093914896725*x6 + x7 =G= 0;
e18.. - 0.744093914896725*x7 + x8 =G= 0;
e19.. - 0.744093914896725*x8 + x9 =G= 0;
e20.. - 0.744093914896725*x9 + x10 =G= 0;
e21.. - 0.744093914896725*x10 + x11 =G= 0;
e22.. - 0.744093914896725*x12 + x13 =G= 0;
e23.. - 0.744093914896725*x13 + x14 =G= 0;
e24.. - 0.744093914896725*x14 + x15 =G= 0;
e25.. - 0.744093914896725*x15 + x16 =G= 0;
e26.. - 0.744093914896725*x16 + x17 =G= 0;
e27.. - 0.744093914896725*x17 + x18 =G= 0;
e28.. - 0.744093914896725*x18 + x19 =G= 0;
e29.. - 0.744093914896725*x19 + x20 =G= 0;
e30.. - 0.744093914896725*x20 + x21 =G= 0;
e31.. - 0.744093914896725*x21 + x22 =G= 0;
e32.. - 0.744093914896725*x23 + x24 =G= 0;
e33.. - 0.744093914896725*x24 + x25 =G= 0;
e34.. - 0.744093914896725*x25 + x26 =G= 0;
e35.. - 0.744093914896725*x26 + x27 =G= 0;
e36.. - 0.744093914896725*x27 + x28 =G= 0;
e37.. - 0.744093914896725*x28 + x29 =G= 0;
e38.. - 0.744093914896725*x29 + x30 =G= 0;
e39.. - 0.744093914896725*x30 + x31 =G= 0;
e40.. - 0.744093914896725*x31 + x32 =G= 0;
e41.. - 0.744093914896725*x32 + x33 =G= 0;
e42.. - 4*x1 + x2 =L= 0.18523;
e43.. - 4*x2 + x3 =L= 0.2442;
e44.. - 4*x3 + x4 =L= 0.30729;
e45.. - 4*x4 + x5 =L= 0.41698;
e46.. - 4*x5 + x6 =L= 0.52802;
e47.. - 4*x6 + x7 =L= 0.65155;
e48.. - 4*x7 + x8 =L= 0.81675;
e49.. - 4*x8 + x9 =L= 0.98667;
e50.. - 4*x9 + x10 =L= 1.15501;
e51.. - 4*x10 + x11 =L= 1.33561;
e52.. - 4*x12 + x13 =L= 0.18523;
e53.. - 4*x13 + x14 =L= 0.2442;
e54.. - 4*x14 + x15 =L= 0.30729;
e55.. - 4*x15 + x16 =L= 0.41698;
e56.. - 4*x16 + x17 =L= 0.52802;
e57.. - 4*x17 + x18 =L= 0.65155;
e58.. - 4*x18 + x19 =L= 0.81675;
e59.. - 4*x19 + x20 =L= 0.98667;
e60.. - 4*x20 + x21 =L= 1.15501;
e61.. - 4*x21 + x22 =L= 1.33561;
e62.. - 4*x23 + x24 =L= 0.18523;
e63.. - 4*x24 + x25 =L= 0.2442;
e64.. - 4*x25 + x26 =L= 0.30729;
e65.. - 4*x26 + x27 =L= 0.41698;
e66.. - 4*x27 + x28 =L= 0.52802;
e67.. - 4*x28 + x29 =L= 0.65155;
e68.. - 4*x29 + x30 =L= 0.81675;
e69.. - 4*x30 + x31 =L= 0.98667;
e70.. - 4*x31 + x32 =L= 1.15501;
e71.. - 4*x32 + x33 =L= 1.33561;
e72.. - 5*x1 - 5*x2 - x34 + x35 =E= 0;
e73.. - 5*x2 - 5*x3 - x35 + x36 =E= 0;
e74.. - 5*x3 - 5*x4 - x36 + x37 =E= 0;
e75.. - 5*x4 - 5*x5 - x37 + x38 =E= 0;
e76.. - 5*x5 - 5*x6 - x38 + x39 =E= 0;
e77.. - 5*x6 - 5*x7 - x39 + x40 =E= 0;
e78.. - 5*x7 - 5*x8 - x40 + x41 =E= 0;
e79.. - 5*x8 - 5*x9 - x41 + x42 =E= 0;
e80.. - 5*x9 - 5*x10 - x42 + x43 =E= 0;
e81.. - 5*x10 - 5*x11 - x43 + x44 =E= 0;
e82.. - 5*x12 - 5*x13 - x45 + x46 =E= 0;
e83.. - 5*x13 - 5*x14 - x46 + x47 =E= 0;
e84.. - 5*x14 - 5*x15 - x47 + x48 =E= 0;
e85.. - 5*x15 - 5*x16 - x48 + x49 =E= 0;
e86.. - 5*x16 - 5*x17 - x49 + x50 =E= 0;
e87.. - 5*x17 - 5*x18 - x50 + x51 =E= 0;
e88.. - 5*x18 - 5*x19 - x51 + x52 =E= 0;
e89.. - 5*x19 - 5*x20 - x52 + x53 =E= 0;
e90.. - 5*x20 - 5*x21 - x53 + x54 =E= 0;
e91.. - 5*x21 - 5*x22 - x54 + x55 =E= 0;
e92.. - 5*x23 - 5*x24 - x56 + x57 =E= 0;
e93.. - 5*x24 - 5*x25 - x57 + x58 =E= 0;
e94.. - 5*x25 - 5*x26 - x58 + x59 =E= 0;
e95.. - 5*x26 - 5*x27 - x59 + x60 =E= 0;
e96.. - 5*x27 - 5*x28 - x60 + x61 =E= 0;
e97.. - 5*x28 - 5*x29 - x61 + x62 =E= 0;
e98.. - 5*x29 - 5*x30 - x62 + x63 =E= 0;
e99.. - 5*x30 - 5*x31 - x63 + x64 =E= 0;
e100.. - 5*x31 - 5*x32 - x64 + x65 =E= 0;
e101.. - 5*x32 - 5*x33 - x65 + x66 =E= 0;
e102.. - 0.850412249705536*x1 - 0.850412249705536*x2 - x67 + x68 =E= 0;
e103.. - 0.850412249705536*x2 - 0.850412249705536*x3 - x68 + x69 =E= 0;
e104.. - 0.850412249705536*x3 - 0.850412249705536*x4 - x69 + x70 =E= 0;
e105.. - 0.850412249705536*x4 - 0.850412249705536*x5 - x70 + x71 =E= 0;
e106.. - 0.850412249705536*x5 - 0.850412249705536*x6 - x71 + x72 =E= 0;
e107.. - 0.850412249705536*x6 - 0.850412249705536*x7 - x72 + x73 =E= 0;
e108.. - 0.850412249705536*x7 - 0.850412249705536*x8 - x73 + x74 =E= 0;
e109.. - 0.850412249705536*x8 - 0.850412249705536*x9 - x74 + x75 =E= 0;
e110.. - 0.850412249705536*x9 - 0.850412249705536*x10 - x75 + x76 =E= 0;
e111.. - 0.850412249705536*x10 - 0.850412249705536*x11 - x76 + x77 =E= 0;
e112.. -(15*(5*x45)**(-0.1)*x12 + 130*(100*x56)**(-0.3)*x23 + 30*x12 + 30*x23
+ 0.613913253540759*(15*(5*x46)**(-0.1)*x13 + 130*(100*x57)**(-0.3)*x24
+ 30*x13 + 30*x24) + 0.376889482873*(15*(5*x47)**(-0.1)*x14 + 130*(100*
x58)**(-0.3)*x25 + 30*x14 + 30*x25) + 0.231377448655858*(15*(5*x48)**(-
0.1)*x15 + 130*(100*x59)**(-0.3)*x26 + 30*x15 + 30*x26) +
0.142045682300278*(15*(5*x49)**(-0.1)*x16 + 130*(100*x60)**(-0.3)*x27 +
30*x16 + 30*x27) + 0.0872037269723804*(15*(5*x50)**(-0.1)*x17 + 130*(100
*x61)**(-0.3)*x28 + 30*x17 + 30*x28) + 0.0535355237464941*(15*(5*x51)**(
-0.1)*x18 + 130*(100*x62)**(-0.3)*x29 + 30*x18 + 30*x29) +
0.0328661675632188*(15*(5*x52)**(-0.1)*x19 + 130*(100*x63)**(-0.3)*x30
+ 30*x19 + 30*x30) + 0.0201769758601514*(15*(5*x53)**(-0.1)*x20 + 130*(
100*x64)**(-0.3)*x31 + 30*x20 + 30*x31) + 0.0123869128969189*(15*(5*x54)
**(-0.1)*x21 + 130*(100*x65)**(-0.3)*x32 + 30*x21 + 30*x32) +
0.00760448999787347*(15*(5*x55)**(-0.1)*x22 + 130*(100*x66)**(-0.3)*x33
+ 30*x22 + 30*x33)) - 40*x1 - 24.5565301416304*x2 - 15.07557931492*x3
- 9.25509794623431*x4 - 5.6818272920111*x5 - 3.48814907889522*x6
- 2.14142094985976*x7 - 1.31464670252875*x8 - 0.807079034406055*x9
- 0.495476515876756*x10 - 0.304179599914939*x11 + objvar =E= 0;
* set non-default bounds
x1.fx = 12.735;
x2.up = 140;
x3.up = 140;
x4.up = 140;
x5.up = 140;
x6.up = 140;
x7.up = 140;
x8.up = 140;
x9.up = 140;
x10.up = 140;
x11.up = 140;
x12.up = 140;
x13.up = 140;
x14.up = 140;
x15.up = 140;
x16.up = 140;
x17.up = 140;
x18.up = 140;
x19.up = 140;
x20.up = 140;
x21.up = 140;
x22.up = 140;
x23.up = 140;
x24.up = 140;
x25.up = 140;
x26.up = 140;
x27.up = 140;
x28.up = 140;
x29.up = 140;
x30.up = 140;
x31.up = 140;
x32.up = 140;
x33.up = 140;
x34.fx = 0.1;
x35.lo = 0.1; x35.up = 10000;
x36.lo = 0.1; x36.up = 10000;
x37.lo = 0.1; x37.up = 10000;
x38.lo = 0.1; x38.up = 10000;
x39.lo = 0.1; x39.up = 10000;
x40.lo = 0.1; x40.up = 10000;
x41.lo = 0.1; x41.up = 10000;
x42.lo = 0.1; x42.up = 10000;
x43.lo = 0.1; x43.up = 10000;
x44.lo = 0.1; x44.up = 10000;
x45.fx = 0.2;
x46.lo = 0.2; x46.up = 10000;
x47.lo = 0.2; x47.up = 10000;
x48.lo = 0.2; x48.up = 10000;
x49.lo = 0.2; x49.up = 10000;
x50.lo = 0.2; x50.up = 10000;
x51.lo = 0.2; x51.up = 10000;
x52.lo = 0.2; x52.up = 10000;
x53.lo = 0.2; x53.up = 10000;
x54.lo = 0.2; x54.up = 10000;
x55.lo = 0.2; x55.up = 10000;
x56.fx = 0.01;
x57.lo = 0.01; x57.up = 10000;
x58.lo = 0.01; x58.up = 10000;
x59.lo = 0.01; x59.up = 10000;
x60.lo = 0.01; x60.up = 10000;
x61.lo = 0.01; x61.up = 10000;
x62.lo = 0.01; x62.up = 10000;
x63.lo = 0.01; x63.up = 10000;
x64.lo = 0.01; x64.up = 10000;
x65.lo = 0.01; x65.up = 10000;
x66.lo = 0.01; x66.up = 10000;
x67.fx = 0;
x68.up = 400;
x69.up = 400;
x70.up = 400;
x71.up = 400;
x72.up = 400;
x73.up = 400;
x74.up = 400;
x75.up = 400;
x76.up = 400;
x77.up = 400;
objvar.lo = 0; objvar.up = 30000;
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