MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance like
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -24643.90415000 (COUENNE) -160.62430510 (GUROBI) -117056.56720000 (LINDO) |
| Referencesⓘ | Bracken, Jerome and McCormick, Garth P, Chapter 8.5. In Bracken, Jerome and McCormick, Garth P, Selected Applications of Nonlinear Programming, John Wiley and Sons, New York, 1968, 90-92. |
| Sourceⓘ | GAMS Model Library model like |
| Applicationⓘ | Statistics |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 9 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 9 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | unknown |
| #Nonzeros in Objectiveⓘ | 9 |
| #Nonlinear Nonzeros in Objectiveⓘ | 9 |
| #Constraintsⓘ | 3 |
| #Linear Constraintsⓘ | 3 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp log mul sqr |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 7 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 81 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 9 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 9 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 9 |
| Average blocksize in Hessian of Lagrangianⓘ | 9.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 3.9894e-01 |
| Maximal coefficientⓘ | 2.6000e+02 |
| Infeasibility of initial pointⓘ | 1.11e-15 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 4 2 2 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 10 10 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 17 8 9 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,objvar;
Positive Variables x4,x5,x6,x7,x8,x9;
Equations e1,e2,e3,e4;
e1.. -(log(0.398942448887604*(x1/x7*exp(-0.5*sqr((95 - x4)/x7)) + x2/x8*exp(-
0.5*sqr((95 - x5)/x8)) + x3/x9*exp(-0.5*sqr((95 - x6)/x9)))) + log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((105 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((105 - x5)/x8)) + x3/x9*exp(-0.5*sqr((105 - x6)/x9)))) + 4*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((110 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((110 - x5)/x8)) + x3/x9*exp(-0.5*sqr((110 - x6)/x9)))) + 4*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((115 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((115 - x5)/x8)) + x3/x9*exp(-0.5*sqr((115 - x6)/x9)))) + 15*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((120 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((120 - x5)/x8)) + x3/x9*exp(-0.5*sqr((120 - x6)/x9)))) + 15*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((125 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((125 - x5)/x8)) + x3/x9*exp(-0.5*sqr((125 - x6)/x9)))) + 15*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((130 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((130 - x5)/x8)) + x3/x9*exp(-0.5*sqr((130 - x6)/x9)))) + 13*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((135 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((135 - x5)/x8)) + x3/x9*exp(-0.5*sqr((135 - x6)/x9)))) + 21*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((140 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((140 - x5)/x8)) + x3/x9*exp(-0.5*sqr((140 - x6)/x9)))) + 12*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((145 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((145 - x5)/x8)) + x3/x9*exp(-0.5*sqr((145 - x6)/x9)))) + 17*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((150 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((150 - x5)/x8)) + x3/x9*exp(-0.5*sqr((150 - x6)/x9)))) + 4*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((155 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((155 - x5)/x8)) + x3/x9*exp(-0.5*sqr((155 - x6)/x9)))) + 20*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((160 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((160 - x5)/x8)) + x3/x9*exp(-0.5*sqr((160 - x6)/x9)))) + 8*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((165 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((165 - x5)/x8)) + x3/x9*exp(-0.5*sqr((165 - x6)/x9)))) + 17*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((170 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((170 - x5)/x8)) + x3/x9*exp(-0.5*sqr((170 - x6)/x9)))) + 8*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((175 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((175 - x5)/x8)) + x3/x9*exp(-0.5*sqr((175 - x6)/x9)))) + 6*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((180 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((180 - x5)/x8)) + x3/x9*exp(-0.5*sqr((180 - x6)/x9)))) + 6*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((185 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((185 - x5)/x8)) + x3/x9*exp(-0.5*sqr((185 - x6)/x9)))) + 7*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((190 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((190 - x5)/x8)) + x3/x9*exp(-0.5*sqr((190 - x6)/x9)))) + 4*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((195 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((195 - x5)/x8)) + x3/x9*exp(-0.5*sqr((195 - x6)/x9)))) + 3*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((200 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((200 - x5)/x8)) + x3/x9*exp(-0.5*sqr((200 - x6)/x9)))) + 3*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((205 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((205 - x5)/x8)) + x3/x9*exp(-0.5*sqr((205 - x6)/x9)))) + 8*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((210 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((210 - x5)/x8)) + x3/x9*exp(-0.5*sqr((210 - x6)/x9)))) + log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((215 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((215 - x5)/x8)) + x3/x9*exp(-0.5*sqr((215 - x6)/x9)))) + 6*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((220 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((220 - x5)/x8)) + x3/x9*exp(-0.5*sqr((220 - x6)/x9)))) + 5*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((230 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((230 - x5)/x8)) + x3/x9*exp(-0.5*sqr((230 - x6)/x9)))) + log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((235 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((235 - x5)/x8)) + x3/x9*exp(-0.5*sqr((235 - x6)/x9)))) + 7*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((240 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((240 - x5)/x8)) + x3/x9*exp(-0.5*sqr((240 - x6)/x9)))) + log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((245 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((245 - x5)/x8)) + x3/x9*exp(-0.5*sqr((245 - x6)/x9)))) + 2*log(
0.398942448887604*(x1/x7*exp(-0.5*sqr((260 - x4)/x7)) + x2/x8*exp(-0.5*
sqr((260 - x5)/x8)) + x3/x9*exp(-0.5*sqr((260 - x6)/x9))))) - objvar =E= 0
;
e2.. x1 + x2 + x3 =E= 1;
e3.. - x4 + x5 =G= 0;
e4.. - x5 + x6 =G= 0;
* set non-default bounds
x1.lo = 0.1;
x2.lo = 0.1;
x3.lo = 0.1;
* set non-default levels
x1.l = 0.333333333333333;
x2.l = 0.333333333333333;
x3.l = 0.333333333333333;
x4.l = 130;
x5.l = 160;
x6.l = 190;
x7.l = 15;
x8.l = 15;
x9.l = 15;
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