MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance pollut
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -5353268.70700000 (ANTIGONE) -5353268.63400000 (BARON) -5353268.62900000 (COUENNE) -5353268.62900000 (LINDO) -5353268.62900000 (SCIP) |
| Referencesⓘ | Mangasarian, Olvi L, Nonlinear Programming, McGraw Hill, New York, 1973. |
| Sourceⓘ | GAMS Model Library model pollut |
| Applicationⓘ | Production |
| Added to libraryⓘ | 31 Jul 2001 |
| Removed from libraryⓘ | 16 Feb 2022 |
| Removed becauseⓘ | Instance is continuous and convex. |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 42 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 40 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | signomial |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 40 |
| #Nonlinear Nonzeros in Objectiveⓘ | 40 |
| #Constraintsⓘ | 8 |
| #Linear Constraintsⓘ | 8 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 126 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 80 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 40 |
| #Blocks in Hessian of Lagrangianⓘ | 20 |
| 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ⓘ | 4.9313e-03 |
| Maximal coefficientⓘ | 1.1146e+01 |
| Infeasibility of initial pointⓘ | 6.631e+05 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 9 3 1 5 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 43 43 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 167 127 40 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,objvar;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9;
e1.. -(9.6*x1**0.879*x21**0.121 + 6.353*x2**0.806*x22**0.194 + 9.818*x3**0.796*
x23**0.204 + 7.371*x4**0.819*x24**0.181 + 10.22*x5**0.829*x25**0.171 +
6.255*x6**0.855*x26**0.145 + 8.149*x7**0.696*x27**0.304 + 7.794*x8**0.854*
x28**0.146 + 8.4*x9**0.827*x29**0.173 + 9.933*x10**0.826*x30**0.174 +
11.069*x11**0.833*x31**0.167 + 6.528*x12**0.808*x32**0.192 + 7.928*x13**
0.884*x33**0.116 + 10.559*x14**0.909*x34**0.091 + 6.606*x15**0.773*x35**
0.227 + 7.153*x16**0.792*x36**0.208 + 11.146*x17**0.849*x37**0.151 + 6.884
*x18**0.801*x38**0.199 + 6.66*x19**0.747*x39**0.253 + 7.929*x20**0.818*x40
**0.182) - objvar =E= 0;
e2.. 0.797744360902256*x1 + 0.208131595282433*x2 + 0.395400943396226*x3
+ 0.00945378151260504*x4 + 0.016020942408377*x5 + 1.32848209209778*x6
+ 0.347442922374429*x7 + 0.534329395413482*x8 + 0.284322678843227*x9
+ 0.283080040526849*x10 + 0.341982864137087*x11 + 0.0127927927927928*x12
+ 0.0437154696132597*x13 + 0.00886939571150097*x14
+ 0.00797702616464582*x15 + 0.00590969455511288*x16
+ 0.0137430167597765*x17 + 0.00493133583021223*x18
+ 0.0273858921161826*x19 + 0.0741242038216561*x20 =L= 153000;
e3.. 0.0854323308270677*x1 + 0.153320918684047*x2 + 0.29127358490566*x3
+ 0.00588235294117647*x4 + 0.00879581151832461*x5 + 0.424161455372371*x6
+ 0.263333333333333*x7 + 0.400764419735928*x8 + 0.126560121765601*x9
+ 0.0462006079027356*x10 + 0.0558139534883721*x11 + 0.528528528528528*x12
+ 0.163052486187845*x13 + 0.329044834307992*x14 + 0.0548819400127632*x15
+ 0.0249667994687915*x16 + 0.0412290502793296*x17
+ 0.00792759051186017*x18 + 0.0174273858921162*x19
+ 0.0200636942675159*x20 =L= 120000;
e4.. 0.281015037593985*x1 + 0.557417752948479*x2 + 0.327830188679245*x3
+ 0.48249299719888*x4 + 0.366492146596859*x5 + 0.266628766344514*x6
+ 0.0589041095890411*x7 + 0.373175816539263*x8 + 2.06088280060883*x9
+ 0.611955420466059*x10 + 0.609547123623011*x11 + 0.691291291291291*x12
+ 0.614640883977901*x13 + 0.260233918128655*x14 + 0.433312061263561*x15
+ 0.412350597609562*x16 + 0.329608938547486*x17 + 0.491260923845194*x18
+ 0.264868603042877*x19 + 0.337579617834395*x20 =L= 250000;
e5.. 0.676221804511278*x1 + 1.05723153320919*x2 + 0.158608490566038*x3
+ 0.112464985994398*x4 + 0.149633507853403*x5 + 0.883001705514497*x6
+ 0.0844748858447489*x7 + 0.6726893676164*x8 + 0.220700152207002*x9
+ 0.932117527862209*x10 + 0.895960832313342*x11 + 0.571771771771772*x12
+ 0.537292817679558*x13 + 0.362573099415205*x14 + 0.314613911933631*x15
+ 0.164674634794157*x16 + 0.256983240223464*x17 + 0.268414481897628*x18
+ 0.208160442600277*x19 + 0.278662420382166*x20 =L= 250000;
e6.. x41 - 0.9*x42 =G= 0;
e7.. x41 - 1.4*x42 =L= 0;
e8.. - x1 - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 - x11 - x12 - x13
- x14 - x15 - x16 - x17 - x18 - x19 - x20 + x41 =E= 0;
e9.. - x21 - x22 - x23 - x24 - x25 - x26 - x27 - x28 - x29 - x30 - x31 - x32
- x33 - x34 - x35 - x36 - x37 - x38 - x39 - x40 + x42 =E= 0;
* set non-default bounds
x1.lo = 17643.6; x1.up = 41168.4;
x2.lo = 12825; x2.up = 29925;
x3.lo = 5053.8; x3.up = 11792.2;
x4.lo = 8323.8; x4.up = 19422.2;
x5.lo = 5082; x5.up = 11858;
x6.lo = 21825; x6.up = 50925;
x7.lo = 39609.6; x7.up = 92422.4;
x8.lo = 48080.4; x8.up = 112187.6;
x9.lo = 796.2; x9.up = 1857.8;
x10.lo = 2648.4; x10.up = 6179.6;
x11.lo = 2225.4; x11.up = 5192.6;
x12.lo = 8697.6; x12.up = 20294.4;
x13.lo = 61439.4; x13.up = 143358.6;
x14.lo = 16804.8; x14.up = 39211.2;
x15.lo = 41588.4; x15.up = 97039.6;
x16.lo = 54008.4; x16.up = 126019.6;
x17.lo = 17616; x17.up = 41104;
x18.lo = 16612.2; x18.up = 38761.8;
x19.lo = 2405.4; x19.up = 5612.6;
x20.lo = 14593.8; x20.up = 34052.2;
x21.lo = 14825.4; x21.up = 34592.6;
x22.lo = 11350.8; x22.up = 26485.2;
x23.lo = 12381.6; x23.up = 28890.4;
x24.lo = 6274.2; x24.up = 14639.8;
x25.lo = 5843.4; x25.up = 13634.6;
x26.lo = 11328; x26.up = 26432;
x27.lo = 26688; x27.up = 62272;
x28.lo = 21915.6; x28.up = 51136.4;
x29.lo = 454.8; x29.up = 1061.2;
x30.lo = 2952.6; x30.up = 6889.4;
x31.lo = 4059.6; x31.up = 9472.4;
x32.lo = 5620.8; x32.up = 13115.2;
x33.lo = 18676.2; x33.up = 43577.8;
x34.lo = 699.6; x34.up = 1632.4;
x35.lo = 35715; x35.up = 83335;
x36.lo = 37828.8; x36.up = 88267.2;
x37.lo = 17903.4; x37.up = 41774.6;
x38.lo = 10167; x38.up = 23723;
x39.lo = 2896.8; x39.up = 6759.2;
x40.lo = 14741.4; x40.up = 34396.6;
* set non-default levels
x1.l = 29406;
x2.l = 21375;
x3.l = 8423;
x4.l = 13873;
x5.l = 8470;
x6.l = 36375;
x7.l = 66016;
x8.l = 80134;
x9.l = 1327;
x10.l = 4414;
x11.l = 3709;
x12.l = 14496;
x13.l = 102399;
x14.l = 28008;
x15.l = 69314;
x16.l = 90014;
x17.l = 29360;
x18.l = 27687;
x19.l = 4009;
x20.l = 24323;
x21.l = 24709;
x22.l = 18918;
x23.l = 20636;
x24.l = 10457;
x25.l = 9739;
x26.l = 18880;
x27.l = 44480;
x28.l = 36526;
x29.l = 758;
x30.l = 4921;
x31.l = 6766;
x32.l = 9368;
x33.l = 31127;
x34.l = 1166;
x35.l = 59525;
x36.l = 63048;
x37.l = 29839;
x38.l = 16945;
x39.l = 4828;
x40.l = 24569;
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