MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance st_e32
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1.43040729 (ANTIGONE) -1.43040729 (BARON) -1.43040728 (LINDO) -1.43040728 (SCIP) -100.00000000 (SHOT) |
| Referencesⓘ | Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Sahinidis, N V, Tawarmalani, M, and Yu, Minrui, Design of alternative refrigerants via global optimization, AIChE Journal, 49:7, 2003, 1761-1775. |
| Sourceⓘ | BARON book instance misc/e32 |
| Added to libraryⓘ | 01 Sep 2002 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 35 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 19 |
| #Nonlinear Variablesⓘ | 33 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 19 |
| Objective Senseⓘ | min |
| Objective typeⓘ | signomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 2 |
| #Nonlinear Nonzeros in Objectiveⓘ | 2 |
| #Constraintsⓘ | 18 |
| #Linear Constraintsⓘ | 6 |
| #Quadratic Constraintsⓘ | 2 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 3 |
| #General Nonlinear Constraintsⓘ | 7 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp log mul power sqr vcpower |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 166 |
| #Nonlinear Nonzeros in Jacobianⓘ | 61 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 439 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 27 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 21 |
| Average blocksize in Hessian of Lagrangianⓘ | 11.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.1000e-03 |
| Maximal coefficientⓘ | 3.1648e+02 |
| Infeasibility of initial pointⓘ | 316.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 19 18 1 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 36 17 0 19 0 0 0 0
* FX 1
*
* Nonzero counts
* Total const NL DLL
* 169 106 63 0
*
* Solve m using MINLP minimizing objvar;
Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
,objvar;
Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
,i18,i19;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19;
e1.. 23.58*i1 + 22.88*i2 + 21.74*i3 + 18.25*i4 - 0.03*i5 + 38.13*i6
+ 66.86*i7 + 93.84*i8 + 92.88*i9 + 76.34*i10 + 22.42*i11 + 31.22*i12
+ 73.23*i13 + 50.17*i14 + 52.82*i15 + 11.74*i16 + 63.56*i17 + 68.78*i18
+ 52.1*i19 - x20 =E= -198.2;
e2.. -x20/(0.584 + 0.0136065*i1 - sqr(0.0141*i1 + 0.0189*i2 + 0.0164*i3 +
0.0067*i4 + 0.0111*i5 + 0.0105*i6 + 0.0133*i7 + 0.0068*i8 + 0.0741*i9 +
0.0204*i10 + 0.0168*i11 + 0.0098*i12 + 0.0243*i13 + 0.0295*i14 + 0.013*i15
+ 0.0169*i16 + 0.0031*i17 + 0.0119*i18 + 0.0019*i19) + 0.0182385*i2 +
0.015826*i3 + 0.0064655*i4 + 0.0107115*i5 + 0.0101325*i6 + 0.0128345*i7 +
0.006562*i8 + 0.0715065*i9 + 0.02316*i10 + 0.016212*i11 + 0.009457*i12 +
0.0234495*i13 + 0.0284675*i14 + 0.012545*i15 + 0.0163085*i16 + 0.0029915*
i17 + 0.0114835*i18 + 0.0018335*i19) + x21 =E= 0;
e3.. -1/(0.113 + 0.014*i1 + 0.0096*i2 + 0.0044*i3 - 0.0011*i4 + 0.0089*i5 +
0.0081*i6 - 0.0025*i7 + 0.0066*i8 - 0.0048*i9 - 0.012*i10 + 0.0017*i11 -
0.0016*i12 - 0.0013*i13 - 0.0013*i14 - 0.005*i15 - 0.0042*i16 - 0.002*i17
- 0.0017*i18 - 0.0019*i19)**2 + x22 =E= 0;
e4.. 8.8*i1 + 7.26*i2 + 5*i3 + 1.76*i4 + 4*i5 + 8.6*i6 + 9*i7 + 8.6*i8
+ 10.7*i9 + 10.7*i10 + 8.4*i11 + 8.4*i12 + 14*i13 + 10.5*i14 + 10.5*i15
+ 7.5*i16 + 10.7*i17 + 8*i18 + 8*i19 - x23 =E= 0;
e5.. 2.373*i1 + 2.226*i2 + 1.691*i3 + 0.636*i4 - 0.67*i5 + 4.532*i6
+ 6.582*i7 + 9.52*i8 + 16.826*i9 + 12.499*i10 + 2.41*i11 + 4.682*i12
+ 10.788*i13 + 6.436*i14 + 6.93*i15 + 1.896*i16 + 6.884*i17 + 6.817*i18
+ 5.984*i19 - x24 =E= -15.3;
e6.. -x20/x21 + x32 =E= 0;
e7.. -272.04/x21 + x30 =E= 0;
e8.. -316.48/x21 + x31 =E= 0;
e9.. -log(x22)*x32/(1 - x32) + x33 =E= 0;
e10.. - 0.4605*x33 + x34 =E= 0.4835;
e11.. -(x33 - (1 + x32)*x34)/(3 + x32)/sqr(1 - x32)/x34 + x35 =E= 0;
e12.. -exp(-(1 + x35*(3 + x30)*POWER(1 - x30,3) - sqr(x30))*x34/x30) + x28
=E= 0;
e13.. -exp(-(1 + x35*(3 + x31)*POWER(1 - x31,3) - sqr(x31))*x34/x31) + x29
=E= 0;
e14.. -x28*x22 + x26 =E= 0;
e15.. -x29*x22 + x27 =E= 0;
e16.. -((1 - x30)/(1 - x32))**0.38*x24 + x25 =E= 0;
e17.. i1 - i3 - 2*i4 + i5 + i6 + i7 + i8 + i9 + i10 + i13 - i16 + i17 =E= 2;
e18.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 =G= 2;
e19.. x25/x23 + objvar =E= 0;
* set non-default bounds
i1.up = 14;
i2.up = 14;
i3.up = 14;
i4.up = 14;
i5.up = 14;
i6.up = 14;
i7.up = 14;
i8.up = 14;
i9.up = 14;
i10.up = 14;
i11.up = 14;
i12.up = 14;
i13.up = 14;
i14.fx = 0;
i15.up = 14;
i16.up = 14;
i17.up = 14;
i18.up = 14;
i19.up = 14;
x20.lo = 1; x20.up = 1000;
x21.lo = 1; x21.up = 1000;
x22.lo = 1; x22.up = 100;
x23.lo = 1; x23.up = 32.2;
x24.lo = 1; x24.up = 100;
x25.lo = 18.4; x25.up = 100;
x26.lo = 1.4; x26.up = 14;
x27.lo = 1.4; x27.up = 14;
x28.lo = 0.001; x28.up = 1;
x29.lo = 0.001; x29.up = 1;
x30.lo = 0.001; x30.up = 1;
x31.lo = 0.001; x31.up = 1;
x32.lo = 0.001; x32.up = 1;
x33.lo = 0.001; x33.up = 10;
x34.lo = 0.001; x34.up = 10;
x35.lo = -10; x35.up = 10;
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