MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance spectra2
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 13.97830588 (ANTIGONE) 13.97830588 (BARON) -1057.38224600 (COUENNE) 13.97830588 (CPLEX) -1187.83533400 (GUROBI) 13.97830588 (LINDO) 13.97830571 (SCIP) 13.97829654 (SHOT) |
| Sourceⓘ | Aldo Vecchietti's Model Collection |
| Applicationⓘ | Parameter estimation in quantitative IR spectroscopy |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 69 |
| #Binary Variablesⓘ | 30 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 30 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 9 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 72 |
| #Linear Constraintsⓘ | 64 |
| #Quadratic Constraintsⓘ | 8 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 399 |
| #Nonlinear Nonzeros in Jacobianⓘ | 240 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 300 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 30 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 10 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 10 |
| Average blocksize in Hessian of Lagrangianⓘ | 10.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 3.0000e-04 |
| Maximal coefficientⓘ | 1.0000e+03 |
| Infeasibility of initial pointⓘ | 108.1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 73 10 33 30 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 70 40 30 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 409 169 240 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,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,objvar,x62,x63,x64,x65,x66,x67,x68,x69
,x70;
Positive Variables 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;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30;
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;
e1.. -((5.02 - 0.0003*x31 - 0.0007*x32 - 0.0066*x33 - 0.0044*x34 - 0.0208*x35
- 0.0518*x36 - 0.0036*x37 - 0.0507*x38 - 0.0905*x39 - 0.0016*x40)*(5.02
- 0.0003*x31 - 0.0007*x32 - 0.0066*x33 - 0.0044*x34 - 0.0208*x35 - 0.0518
*x36 - 0.0036*x37 - 0.0507*x38 - 0.0905*x39 - 0.0016*x40) + (0.97 - 0.0003
*x41 - 0.0007*x42 - 0.0066*x43 - 0.0044*x44 - 0.0208*x45 - 0.0518*x46 -
0.0036*x47 - 0.0507*x48 - 0.0905*x49 - 0.0016*x50)*(0.97 - 0.0003*x41 -
0.0007*x42 - 0.0066*x43 - 0.0044*x44 - 0.0208*x45 - 0.0518*x46 - 0.0036*
x47 - 0.0507*x48 - 0.0905*x49 - 0.0016*x50) + (-0.0003*x51 - 0.0007*x52 -
0.0066*x53 - 0.0044*x54 - 0.0208*x55 - 0.0518*x56 - 0.0036*x57 - 0.0507*
x58 - 0.0905*x59 - 0.0016*x60)*(-0.0003*x51 - 0.0007*x52 - 0.0066*x53 -
0.0044*x54 - 0.0208*x55 - 0.0518*x56 - 0.0036*x57 - 0.0507*x58 - 0.0905*
x59 - 0.0016*x60)) + x62 =E= 0;
e2.. -((2.04 - 0.0764*x31 - 0.0003*x32 - 0.0789*x33 - 0.0186*x34 - 0.0605*x35
- 0.1656*x36 - 0.0035*x37 - 0.0361*x38 - 0.06*x39 - 0.0209*x40)*(2.04 -
0.0764*x31 - 0.0003*x32 - 0.0789*x33 - 0.0186*x34 - 0.0605*x35 - 0.1656*
x36 - 0.0035*x37 - 0.0361*x38 - 0.06*x39 - 0.0209*x40) + (3.51 - 0.0764*
x41 - 0.0003*x42 - 0.0789*x43 - 0.0186*x44 - 0.0605*x45 - 0.1656*x46 -
0.0035*x47 - 0.0361*x48 - 0.06*x49 - 0.0209*x50)*(3.51 - 0.0764*x41 -
0.0003*x42 - 0.0789*x43 - 0.0186*x44 - 0.0605*x45 - 0.1656*x46 - 0.0035*
x47 - 0.0361*x48 - 0.06*x49 - 0.0209*x50) + (2.2 - 0.0764*x51 - 0.0003*x52
- 0.0789*x53 - 0.0186*x54 - 0.0605*x55 - 0.1656*x56 - 0.0035*x57 - 0.0361
*x58 - 0.06*x59 - 0.0209*x60)*(2.2 - 0.0764*x51 - 0.0003*x52 - 0.0789*x53
- 0.0186*x54 - 0.0605*x55 - 0.1656*x56 - 0.0035*x57 - 0.0361*x58 - 0.06*
x59 - 0.0209*x60)) + x63 =E= 0;
e3.. -((3.53 - 0.0318*x31 - 0.0004*x32 - 0.0275*x33 - 0.018*x34 - 0.0601*x35 -
0.1491*x36 - 0.0032*x37 - 0.0433*x38 - 0.0754*x39 - 0.0063*x40)*(3.53 -
0.0318*x31 - 0.0004*x32 - 0.0275*x33 - 0.018*x34 - 0.0601*x35 - 0.1491*x36
- 0.0032*x37 - 0.0433*x38 - 0.0754*x39 - 0.0063*x40) + (3.51 - 0.0318*x41
- 0.0004*x42 - 0.0275*x43 - 0.018*x44 - 0.0601*x45 - 0.1491*x46 - 0.0032*
x47 - 0.0433*x48 - 0.0754*x49 - 0.0063*x50)*(3.51 - 0.0318*x41 - 0.0004*
x42 - 0.0275*x43 - 0.018*x44 - 0.0601*x45 - 0.1491*x46 - 0.0032*x47 -
0.0433*x48 - 0.0754*x49 - 0.0063*x50) + (0.8 - 0.0318*x51 - 0.0004*x52 -
0.0275*x53 - 0.018*x54 - 0.0601*x55 - 0.1491*x56 - 0.0032*x57 - 0.0433*x58
- 0.0754*x59 - 0.0063*x60)*(0.8 - 0.0318*x51 - 0.0004*x52 - 0.0275*x53 -
0.018*x54 - 0.0601*x55 - 0.1491*x56 - 0.0032*x57 - 0.0433*x58 - 0.0754*x59
- 0.0063*x60)) + x64 =E= 0;
e4.. -((7.02 - 0.0007*x31 - 0.0009*x32 - 0.0043*x33 - 0.0179*x34 - 0.0604*x35
- 0.1385*x36 - 0.0051*x37 - 0.0635*x38 - 0.1098*x39 - 0.001*x40)*(7.02 -
0.0007*x31 - 0.0009*x32 - 0.0043*x33 - 0.0179*x34 - 0.0604*x35 - 0.1385*
x36 - 0.0051*x37 - 0.0635*x38 - 0.1098*x39 - 0.001*x40) + (3.51 - 0.0007*
x41 - 0.0009*x42 - 0.0043*x43 - 0.0179*x44 - 0.0604*x45 - 0.1385*x46 -
0.0051*x47 - 0.0635*x48 - 0.1098*x49 - 0.001*x50)*(3.51 - 0.0007*x41 -
0.0009*x42 - 0.0043*x43 - 0.0179*x44 - 0.0604*x45 - 0.1385*x46 - 0.0051*
x47 - 0.0635*x48 - 0.1098*x49 - 0.001*x50) + (-0.0007*x51 - 0.0009*x52 -
0.0043*x53 - 0.0179*x54 - 0.0604*x55 - 0.1385*x56 - 0.0051*x57 - 0.0635*
x58 - 0.1098*x59 - 0.001*x60)*(-0.0007*x51 - 0.0009*x52 - 0.0043*x53 -
0.0179*x54 - 0.0604*x55 - 0.1385*x56 - 0.0051*x57 - 0.0635*x58 - 0.1098*
x59 - 0.001*x60)) + x65 =E= 0;
e5.. -((-0.0534*x31 - 0.0005*x32 - 0.0704*x33 - 0.0351*x34 - 0.0981*x35 -
0.2389*x36 - 0.0015*x37 - 0.0048*x38 - 0.0038*x39 - 0.0132*x40)*(-0.0534*
x31 - 0.0005*x32 - 0.0704*x33 - 0.0351*x34 - 0.0981*x35 - 0.2389*x36 -
0.0015*x37 - 0.0048*x38 - 0.0038*x39 - 0.0132*x40) + (7 - 0.0534*x41 -
0.0005*x42 - 0.0704*x43 - 0.0351*x44 - 0.0981*x45 - 0.2389*x46 - 0.0015*
x47 - 0.0048*x48 - 0.0038*x49 - 0.0132*x50)*(7 - 0.0534*x41 - 0.0005*x42
- 0.0704*x43 - 0.0351*x44 - 0.0981*x45 - 0.2389*x46 - 0.0015*x47 - 0.0048
*x48 - 0.0038*x49 - 0.0132*x50) + (1.4 - 0.0534*x51 - 0.0005*x52 - 0.0704*
x53 - 0.0351*x54 - 0.0981*x55 - 0.2389*x56 - 0.0015*x57 - 0.0048*x58 -
0.0038*x59 - 0.0132*x60)*(1.4 - 0.0534*x51 - 0.0005*x52 - 0.0704*x53 -
0.0351*x54 - 0.0981*x55 - 0.2389*x56 - 0.0015*x57 - 0.0048*x58 - 0.0038*
x59 - 0.0132*x60)) + x66 =E= 0;
e6.. -((10.16 - 0.0773*x31 - 0.0009*x32 - 0.0683*x33 - 0.0024*x34 - 0.0025*x35
- 0.0248*x36 - 0.0094*x37 - 0.0891*x38 - 0.1443*x39 - 0.0203*x40)*(10.16
- 0.0773*x31 - 0.0009*x32 - 0.0683*x33 - 0.0024*x34 - 0.0025*x35 - 0.0248
*x36 - 0.0094*x37 - 0.0891*x38 - 0.1443*x39 - 0.0203*x40) + (-0.0773*x41
- 0.0009*x42 - 0.0683*x43 - 0.0024*x44 - 0.0025*x45 - 0.0248*x46 - 0.0094
*x47 - 0.0891*x48 - 0.1443*x49 - 0.0203*x50)*(-0.0773*x41 - 0.0009*x42 -
0.0683*x43 - 0.0024*x44 - 0.0025*x45 - 0.0248*x46 - 0.0094*x47 - 0.0891*
x48 - 0.1443*x49 - 0.0203*x50) + (2.2 - 0.0773*x51 - 0.0009*x52 - 0.0683*
x53 - 0.0024*x54 - 0.0025*x55 - 0.0248*x56 - 0.0094*x57 - 0.0891*x58 -
0.1443*x59 - 0.0203*x60)*(2.2 - 0.0773*x51 - 0.0009*x52 - 0.0683*x53 -
0.0024*x54 - 0.0025*x55 - 0.0248*x56 - 0.0094*x57 - 0.0891*x58 - 0.1443*
x59 - 0.0203*x60)) + x67 =E= 0;
e7.. -((1.04 - 0.0536*x31 - 0.0005*x32 - 0.0842*x33 - 0.0108*x34 - 0.0394*x35
- 0.1122*x36 - 0.0015*x37 - 0.0213*x38 - 0.042*x39 - 0.0139*x40)*(1.04 -
0.0536*x31 - 0.0005*x32 - 0.0842*x33 - 0.0108*x34 - 0.0394*x35 - 0.1122*
x36 - 0.0015*x37 - 0.0213*x38 - 0.042*x39 - 0.0139*x40) + (2.01 - 0.0536*
x41 - 0.0005*x42 - 0.0842*x43 - 0.0108*x44 - 0.0394*x45 - 0.1122*x46 -
0.0015*x47 - 0.0213*x48 - 0.042*x49 - 0.0139*x50)*(2.01 - 0.0536*x41 -
0.0005*x42 - 0.0842*x43 - 0.0108*x44 - 0.0394*x45 - 0.1122*x46 - 0.0015*
x47 - 0.0213*x48 - 0.042*x49 - 0.0139*x50) + (1.4 - 0.0536*x51 - 0.0005*
x52 - 0.0842*x53 - 0.0108*x54 - 0.0394*x55 - 0.1122*x56 - 0.0015*x57 -
0.0213*x58 - 0.042*x59 - 0.0139*x60)*(1.4 - 0.0536*x51 - 0.0005*x52 -
0.0842*x53 - 0.0108*x54 - 0.0394*x55 - 0.1122*x56 - 0.0015*x57 - 0.0213*
x58 - 0.042*x59 - 0.0139*x60)) + x68 =E= 0;
e8.. -((2.04 - 0.032*x31 - 0.0003*x32 - 0.0309*x33 - 0.0052*x34 - 0.0221*x35 -
0.0633*x36 - 0.0024*x37 - 0.031*x38 - 0.0574*x39 - 0.0057*x40)*(2.04 -
0.032*x31 - 0.0003*x32 - 0.0309*x33 - 0.0052*x34 - 0.0221*x35 - 0.0633*x36
- 0.0024*x37 - 0.031*x38 - 0.0574*x39 - 0.0057*x40) + (0.97 - 0.032*x41
- 0.0003*x42 - 0.0309*x43 - 0.0052*x44 - 0.0221*x45 - 0.0633*x46 - 0.0024
*x47 - 0.031*x48 - 0.0574*x49 - 0.0057*x50)*(0.97 - 0.032*x41 - 0.0003*x42
- 0.0309*x43 - 0.0052*x44 - 0.0221*x45 - 0.0633*x46 - 0.0024*x47 - 0.031*
x48 - 0.0574*x49 - 0.0057*x50) + (0.8 - 0.032*x51 - 0.0003*x52 - 0.0309*
x53 - 0.0052*x54 - 0.0221*x55 - 0.0633*x56 - 0.0024*x57 - 0.031*x58 -
0.0574*x59 - 0.0057*x60)*(0.8 - 0.032*x51 - 0.0003*x52 - 0.0309*x53 -
0.0052*x54 - 0.0221*x55 - 0.0633*x56 - 0.0024*x57 - 0.031*x58 - 0.0574*x59
- 0.0057*x60)) + x69 =E= 0;
e9.. x31 =G= 0;
e10.. x32 =G= 0;
e11.. x33 =G= 0;
e12.. x34 =G= 0;
e13.. x35 =G= 0;
e14.. x36 =G= 0;
e15.. x37 =G= 0;
e16.. x38 =G= 0;
e17.. x39 =G= 0;
e18.. x40 =G= 0;
e19.. x41 =G= 0;
e20.. x42 =G= 0;
e21.. x43 =G= 0;
e22.. x44 =G= 0;
e23.. x45 =G= 0;
e24.. x46 =G= 0;
e25.. x47 =G= 0;
e26.. x48 =G= 0;
e27.. x49 =G= 0;
e28.. x50 =G= 0;
e29.. x51 =G= 0;
e30.. x52 =G= 0;
e31.. x53 =G= 0;
e32.. x54 =G= 0;
e33.. x55 =G= 0;
e34.. x56 =G= 0;
e35.. x57 =G= 0;
e36.. x58 =G= 0;
e37.. x59 =G= 0;
e38.. x60 =G= 0;
e39.. - 1000*b1 + x31 =L= 0;
e40.. - 1000*b2 + x32 =L= 0;
e41.. - 1000*b3 + x33 =L= 0;
e42.. - 1000*b4 + x34 =L= 0;
e43.. - 1000*b5 + x35 =L= 0;
e44.. - 1000*b6 + x36 =L= 0;
e45.. - 1000*b7 + x37 =L= 0;
e46.. - 1000*b8 + x38 =L= 0;
e47.. - 1000*b9 + x39 =L= 0;
e48.. - 1000*b10 + x40 =L= 0;
e49.. - 1000*b11 + x41 =L= 0;
e50.. - 1000*b12 + x42 =L= 0;
e51.. - 1000*b13 + x43 =L= 0;
e52.. - 1000*b14 + x44 =L= 0;
e53.. - 1000*b15 + x45 =L= 0;
e54.. - 1000*b16 + x46 =L= 0;
e55.. - 1000*b17 + x47 =L= 0;
e56.. - 1000*b18 + x48 =L= 0;
e57.. - 1000*b19 + x49 =L= 0;
e58.. - 1000*b20 + x50 =L= 0;
e59.. - 1000*b21 + x51 =L= 0;
e60.. - 1000*b22 + x52 =L= 0;
e61.. - 1000*b23 + x53 =L= 0;
e62.. - 1000*b24 + x54 =L= 0;
e63.. - 1000*b25 + x55 =L= 0;
e64.. - 1000*b26 + x56 =L= 0;
e65.. - 1000*b27 + x57 =L= 0;
e66.. - 1000*b28 + x58 =L= 0;
e67.. - 1000*b29 + x59 =L= 0;
e68.. - 1000*b30 + x60 =L= 0;
e69.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 =G= 0;
e70.. b11 + b12 + b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 =G= 0;
e71.. b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =G= 0;
e72.. - b1 - b2 - b3 - b4 - b5 - b6 - b7 - b8 - b9 - b10 - b11 - b12 - b13
- b14 - b15 - b16 - b17 - b18 - b19 - b20 - b21 - b22 - b23 - b24 - b25
- b26 - b27 - b28 - b29 - b30 + x70 =E= 0;
e73.. objvar - x62 - x63 - x64 - x65 - x66 - x67 - x68 - x69 - 2*x70 =E= 0;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc