MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex8_2_1b
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -979.17827480 (ANTIGONE) -979.17827560 (BARON) -979.17827380 (COUENNE) -979.17827380 (LINDO) -979.17910640 (SCIP) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Grossmann, I E and Sargent, R, Optimal Design of Multipurpose Chemical Plants, Industrial and Engineering Chemistry Process Design and Development, 18:2, 1979, 343-348. Harding, S T and Floudas, C A, Global Optimization in Multiproduct and Multipurpose Batch Design Under Uncertainty, Industrial and Engineering Chemistry Research, 36:5, 1997, 1644-1664. |
| Sourceⓘ | Test Problem ex8.2.1 of Chapter 8 of Floudas e.a. handbook with added variable bounds and common multiplicative sub-expression exp(data-b(i)) replaced |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 57 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 57 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 53 |
| #Nonlinear Nonzeros in Objectiveⓘ | 3 |
| #Constraintsⓘ | 33 |
| #Linear Constraintsⓘ | 6 |
| #Quadratic Constraintsⓘ | 25 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 2 |
| Operands in Gen. Nonlin. Functionsⓘ | exp |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 116 |
| #Nonlinear Nonzeros in Jacobianⓘ | 102 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 105 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 5 |
| #Blocks in Hessian of Lagrangianⓘ | 7 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 26 |
| Average blocksize in Hessian of Lagrangianⓘ | 8.142857 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.5471e-06 |
| Maximal coefficientⓘ | 1.0000e+01 |
| Infeasibility of initial pointⓘ | 0.1707 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 34 3 6 25 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 58 58 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 170 65 105 0
*
* Solve m using NLP minimizing objvar;
Variables objvar,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,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
,x53,x54,x55,x56,x57,x58;
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;
e1.. -0.3*(10*exp(0.6*x2) + 10*exp(0.6*x3) + 10*exp(0.6*x4)) + objvar
+ 1.54711033913716E-6*x5 + 0.000219040316990534*x6
+ 0.00264813118267794*x7 + 0.000219040316990534*x8
+ 1.54711033913716E-6*x9 + 0.000219040316990533*x10
+ 0.0310117896917886*x11 + 0.374923157717238*x12 + 0.0310117896917886*x13
+ 0.000219040316990532*x14 + 0.00264813118267793*x15
+ 0.374923157717237*x16 + 4.5327075795914*x17 + 0.374923157717237*x18
+ 0.00264813118267791*x19 + 0.000219040316990532*x20
+ 0.0310117896917884*x21 + 0.374923157717236*x22 + 0.0310117896917884*x23
+ 0.000219040316990531*x24 + 1.54711033913713E-6*x25
+ 0.000219040316990529*x26 + 0.00264813118267789*x27
+ 0.000219040316990529*x28 + 1.54711033913712E-6*x29
+ 1.9690495225382E-6*x30 + 0.000278778585260679*x31
+ 0.00337034877795374*x32 + 0.000278778585260679*x33
+ 1.9690495225382E-6*x34 + 0.000278778585260679*x35
+ 0.0394695505168218*x36 + 0.477174928003758*x37 + 0.0394695505168218*x38
+ 0.000278778585260677*x39 + 0.00337034877795372*x40
+ 0.477174928003756*x41 + 5.7689005558436*x42 + 0.477174928003756*x43
+ 0.00337034877795371*x44 + 0.000278778585260677*x45
+ 0.0394695505168216*x46 + 0.477174928003755*x47 + 0.0394695505168216*x48
+ 0.000278778585260676*x49 + 1.96904952253816E-6*x50
+ 0.000278778585260674*x51 + 0.00337034877795367*x52
+ 0.000278778585260674*x53 + 1.96904952253816E-6*x54 =E= 0;
e2.. x2 - x55 =G= 0.693147180559945;
e3.. x3 - x55 =G= 1.09861228866811;
e4.. x4 - x55 =G= 1.38629436111989;
e5.. x2 - x56 =G= 1.38629436111989;
e6.. x3 - x56 =G= 1.79175946922805;
e7.. x4 - x56 =G= 1.09861228866811;
e8.. x5*x57 + x30*x58 =L= 8;
e9.. x6*x57 + x31*x58 =L= 8;
e10.. x7*x57 + x32*x58 =L= 8;
e11.. x8*x57 + x33*x58 =L= 8;
e12.. x9*x57 + x34*x58 =L= 8;
e13.. x10*x57 + x35*x58 =L= 8;
e14.. x11*x57 + x36*x58 =L= 8;
e15.. x12*x57 + x37*x58 =L= 8;
e16.. x13*x57 + x38*x58 =L= 8;
e17.. x14*x57 + x39*x58 =L= 8;
e18.. x15*x57 + x40*x58 =L= 8;
e19.. x16*x57 + x41*x58 =L= 8;
e20.. x17*x57 + x42*x58 =L= 8;
e21.. x18*x57 + x43*x58 =L= 8;
e22.. x19*x57 + x44*x58 =L= 8;
e23.. x20*x57 + x45*x58 =L= 8;
e24.. x21*x57 + x46*x58 =L= 8;
e25.. x22*x57 + x47*x58 =L= 8;
e26.. x23*x57 + x48*x58 =L= 8;
e27.. x24*x57 + x49*x58 =L= 8;
e28.. x25*x57 + x50*x58 =L= 8;
e29.. x26*x57 + x51*x58 =L= 8;
e30.. x27*x57 + x52*x58 =L= 8;
e31.. x28*x57 + x53*x58 =L= 8;
e32.. x29*x57 + x54*x58 =L= 8;
e33.. -exp(2.99573227355399 - x55) + x57 =E= 0;
e34.. -exp(2.77258872223978 - x56) + x58 =E= 0;
* set non-default bounds
x2.lo = 6.21460809842219; x2.up = 8.41183267575841;
x3.lo = 6.21460809842219; x3.up = 8.41183267575841;
x4.lo = 6.21460809842219; x4.up = 8.41183267575841;
x5.lo = 160; x5.up = 163.752806164;
x6.lo = 160; x6.up = 163.752806164;
x7.lo = 160; x7.up = 163.752806164;
x8.lo = 160; x8.up = 163.752806164;
x9.lo = 160; x9.up = 163.752806164;
x10.lo = 160; x10.up = 178.461227596;
x11.lo = 160; x11.up = 178.461227596;
x12.lo = 160; x12.up = 178.461227596;
x13.lo = 160; x13.up = 178.461227596;
x14.lo = 160; x14.up = 178.461227596;
x15.lo = 160; x15.up = 200;
x16.lo = 160; x16.up = 200;
x17.lo = 160; x17.up = 200;
x18.lo = 160; x18.up = 200;
x19.lo = 160; x19.up = 200;
x20.lo = 160; x20.up = 221.538772404;
x21.lo = 160; x21.up = 221.538772404;
x22.lo = 160; x22.up = 221.538772404;
x23.lo = 160; x23.up = 221.538772404;
x24.lo = 160; x24.up = 221.538772404;
x25.lo = 160; x25.up = 236.247193836;
x26.lo = 160; x26.up = 236.247193836;
x27.lo = 160; x27.up = 236.247193836;
x28.lo = 160; x28.up = 236.247193836;
x29.lo = 160; x29.up = 236.247193836;
x30.lo = 60; x30.up = 63.752806164;
x31.lo = 60; x31.up = 78.461227596;
x32.lo = 60; x32.up = 100;
x33.lo = 60; x33.up = 121.538772404;
x34.lo = 60; x34.up = 136.247193836;
x35.lo = 60; x35.up = 63.752806164;
x36.lo = 60; x36.up = 78.461227596;
x37.lo = 60; x37.up = 100;
x38.lo = 60; x38.up = 121.538772404;
x39.lo = 60; x39.up = 136.247193836;
x40.lo = 60; x40.up = 63.752806164;
x41.lo = 60; x41.up = 78.461227596;
x42.lo = 60; x42.up = 100;
x43.lo = 60; x43.up = 121.538772404;
x44.lo = 60; x44.up = 136.247193836;
x45.lo = 60; x45.up = 63.752806164;
x46.lo = 60; x46.up = 78.461227596;
x47.lo = 60; x47.up = 100;
x48.lo = 60; x48.up = 121.538772404;
x49.lo = 60; x49.up = 136.247193836;
x50.lo = 60; x50.up = 63.752806164;
x51.lo = 60; x51.up = 78.461227596;
x52.lo = 60; x52.up = 100;
x53.lo = 60; x53.up = 121.538772404;
x54.lo = 60; x54.up = 136.247193836;
x55.lo = 4.8283137373023; x55.up = 7.02553831463852;
x56.lo = 4.42284862919414; x56.up = 6.62007320653036;
x57.lo = 0.0177777777777778; x57.up = 0.16;
x58.lo = 0.0213333333333333; x58.up = 0.192;
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