MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance ex3
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | |
| Referencesⓘ | Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339. |
| Sourceⓘ | MINOPT Model Library model duran86-3.dat, Aldo Vecchietti's Model Collection |
| Applicationⓘ | Process selection |
| Added to libraryⓘ | 01 May 2001 |
| Removed from libraryⓘ | 31 May 2014 |
| Removed becauseⓘ | Variant of ex3pb with some variable bounds missing |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 32 |
| #Binary Variablesⓘ | 8 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 5 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 22 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 31 |
| #Linear Constraintsⓘ | 26 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 5 |
| Operands in Gen. Nonlin. Functionsⓘ | exp |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 77 |
| #Nonlinear Nonzeros in Jacobianⓘ | 5 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 5 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 5 |
| #Blocks in Hessian of Lagrangianⓘ | 5 |
| 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ⓘ | 4.0000e-01 |
| Maximal coefficientⓘ | 8.0000e+01 |
| Infeasibility of initial pointⓘ | 2 |
$offlisting
* MINLP written by GAMS Convert at 04/18/01 12:06:38
*
* Equation counts
* Total E G L N X
* 32 18 2 12 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 33 25 8 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 100 95 5 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,objvar;
Positive Variables x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23
,x24,x25,x26,x27,x28,x29,x30,x31,x32;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8;
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;
e1.. exp(x10) - x9 =E= 1;
e2.. exp(0.833333333333333*x12) - x11 =E= 1;
e3.. - x15 + 1.5*x16 + x17 =E= 0;
e4.. 1.25*x19 - x20 + 1.25*x21 =E= 0;
e5.. x22 - 2*x23 =E= 0;
e6.. exp(0.666666666666667*x27) - x26 =E= 1;
e7.. exp(x29) - x28 =E= 1;
e8.. exp(x25) - x17 - x24 =E= 1;
e9.. x20 - x26 - x28 =E= 0;
e10.. - x16 - x23 + x24 - x32 =E= 0;
e11.. x18 - x19 - x22 =E= 0;
e12.. x10 + x12 - x13 - x18 =E= 0;
e13.. x13 - x14 - x15 =E= 0;
e14.. - x27 - x29 + x30 =E= 0;
e15.. - x21 + x30 - x31 =E= 0;
e16.. x17 - 0.8*x24 =L= 0;
e17.. x17 - 0.4*x24 =G= 0;
e18.. x19 - 5*x21 =L= 0;
e19.. x19 - 2*x21 =G= 0;
e20.. - 10*b8 + x9 =L= 0;
e21.. - 10*b1 + x11 =L= 0;
e22.. - 10*b2 + x16 =L= 0;
e23.. - 10*b3 + x19 + x21 =L= 0;
e24.. - 10*b4 + x22 =L= 0;
e25.. - 10*b5 + x26 =L= 0;
e26.. - 10*b6 + x28 =L= 0;
e27.. - 10*b7 + x17 + x24 =L= 0;
e28.. b1 + b8 =E= 1;
e29.. b3 + b4 =L= 1;
e30.. - b3 + b5 + b6 =E= 0;
e31.. b2 - b7 =L= 0;
e32.. - 8*b1 - 6*b2 - 10*b3 - 6*b4 - 7*b5 - 4*b6 - 5*b7 - 5*b8 - x9 + 10*x10
- x11 + 15*x12 + 40*x16 - 15*x17 - 15*x21 - 80*x24 + 65*x25 - 25*x26
+ 60*x27 - 35*x28 + 80*x29 + 35*x32 + objvar =E= 122;
* set non default bounds
x10.up = 2;
x12.up = 2;
x16.up = 2;
x17.up = 1;
x21.up = 1;
x24.up = 2;
x26.up = 2;
x28.up = 2;
x32.up = 3;
$if set nostart $goto modeldef
* set non default levels
x9.l = 2;
x10.l = 1.5;
x13.l = 0.75;
x14.l = 0.5;
x15.l = 0.5;
x16.l = 0.75;
x18.l = 1.5;
x19.l = 1.34;
x20.l = 2;
x25.l = 0.75;
x27.l = 1.5;
x30.l = 1.7;
x31.l = 1.5;
x32.l = 0.5;
* set non default marginals
$label modeldef
Model m / all /;
m.limrow=0; m.limcol=0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2024-04-02 Git hash: 1dd5fb9b