MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance ex8_2_4a
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | |
| 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. 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 ex8.2.4 of Chapter 8 of Floudas e.a. handbook with added variable bounds |
| Added to libraryⓘ | 31 Jul 2001 |
| Removed from libraryⓘ | 14 Aug 2014 |
| Removed becauseⓘ | Variant of ex8_2_4b with x57..x62 not substituted out |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 55 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 55 |
| #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ⓘ | 81 |
| #Linear Constraintsⓘ | 6 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 75 |
| Operands in Gen. Nonlin. Functionsⓘ | exp mul |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 312 |
| #Nonlinear Nonzeros in Jacobianⓘ | 300 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 105 |
| #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ⓘ | 26 |
| Average blocksize in Hessian of Lagrangianⓘ | 11.0 |
| #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ⓘ | 20.48 |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 82 1 6 75 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 56 56 0 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 366 63 303 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;
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,e74,e75,e76,e77,e78,e79,e80,e81,e82;
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.. exp(2.07944154167984 - x55)*x5 + exp(2.77258872223978 - x56)*x30 =L= 8;
e9.. exp(2.07944154167984 - x55)*x6 + exp(2.77258872223978 - x56)*x31 =L= 8;
e10.. exp(2.07944154167984 - x55)*x7 + exp(2.77258872223978 - x56)*x32 =L= 8;
e11.. exp(2.07944154167984 - x55)*x8 + exp(2.77258872223978 - x56)*x33 =L= 8;
e12.. exp(2.07944154167984 - x55)*x9 + exp(2.77258872223978 - x56)*x34 =L= 8;
e13.. exp(2.07944154167984 - x55)*x10 + exp(2.77258872223978 - x56)*x35 =L= 8;
e14.. exp(2.07944154167984 - x55)*x11 + exp(2.77258872223978 - x56)*x36 =L= 8;
e15.. exp(2.07944154167984 - x55)*x12 + exp(2.77258872223978 - x56)*x37 =L= 8;
e16.. exp(2.07944154167984 - x55)*x13 + exp(2.77258872223978 - x56)*x38 =L= 8;
e17.. exp(2.07944154167984 - x55)*x14 + exp(2.77258872223978 - x56)*x39 =L= 8;
e18.. exp(2.07944154167984 - x55)*x15 + exp(2.77258872223978 - x56)*x40 =L= 8;
e19.. exp(2.07944154167984 - x55)*x16 + exp(2.77258872223978 - x56)*x41 =L= 8;
e20.. exp(2.07944154167984 - x55)*x17 + exp(2.77258872223978 - x56)*x42 =L= 8;
e21.. exp(2.07944154167984 - x55)*x18 + exp(2.77258872223978 - x56)*x43 =L= 8;
e22.. exp(2.07944154167984 - x55)*x19 + exp(2.77258872223978 - x56)*x44 =L= 8;
e23.. exp(2.07944154167984 - x55)*x20 + exp(2.77258872223978 - x56)*x45 =L= 8;
e24.. exp(2.07944154167984 - x55)*x21 + exp(2.77258872223978 - x56)*x46 =L= 8;
e25.. exp(2.07944154167984 - x55)*x22 + exp(2.77258872223978 - x56)*x47 =L= 8;
e26.. exp(2.07944154167984 - x55)*x23 + exp(2.77258872223978 - x56)*x48 =L= 8;
e27.. exp(2.07944154167984 - x55)*x24 + exp(2.77258872223978 - x56)*x49 =L= 8;
e28.. exp(2.07944154167984 - x55)*x25 + exp(2.77258872223978 - x56)*x50 =L= 8;
e29.. exp(2.07944154167984 - x55)*x26 + exp(2.77258872223978 - x56)*x51 =L= 8;
e30.. exp(2.07944154167984 - x55)*x27 + exp(2.77258872223978 - x56)*x52 =L= 8;
e31.. exp(2.07944154167984 - x55)*x28 + exp(2.77258872223978 - x56)*x53 =L= 8;
e32.. exp(2.07944154167984 - x55)*x29 + exp(2.77258872223978 - x56)*x54 =L= 8;
e33.. exp(2.99573227355399 - x55)*x5 + exp(1.38629436111989 - x56)*x30 =L= 8;
e34.. exp(2.99573227355399 - x55)*x6 + exp(1.38629436111989 - x56)*x31 =L= 8;
e35.. exp(2.99573227355399 - x55)*x7 + exp(1.38629436111989 - x56)*x32 =L= 8;
e36.. exp(2.99573227355399 - x55)*x8 + exp(1.38629436111989 - x56)*x33 =L= 8;
e37.. exp(2.99573227355399 - x55)*x9 + exp(1.38629436111989 - x56)*x34 =L= 8;
e38.. exp(2.99573227355399 - x55)*x10 + exp(1.38629436111989 - x56)*x35 =L= 8;
e39.. exp(2.99573227355399 - x55)*x11 + exp(1.38629436111989 - x56)*x36 =L= 8;
e40.. exp(2.99573227355399 - x55)*x12 + exp(1.38629436111989 - x56)*x37 =L= 8;
e41.. exp(2.99573227355399 - x55)*x13 + exp(1.38629436111989 - x56)*x38 =L= 8;
e42.. exp(2.99573227355399 - x55)*x14 + exp(1.38629436111989 - x56)*x39 =L= 8;
e43.. exp(2.99573227355399 - x55)*x15 + exp(1.38629436111989 - x56)*x40 =L= 8;
e44.. exp(2.99573227355399 - x55)*x16 + exp(1.38629436111989 - x56)*x41 =L= 8;
e45.. exp(2.99573227355399 - x55)*x17 + exp(1.38629436111989 - x56)*x42 =L= 8;
e46.. exp(2.99573227355399 - x55)*x18 + exp(1.38629436111989 - x56)*x43 =L= 8;
e47.. exp(2.99573227355399 - x55)*x19 + exp(1.38629436111989 - x56)*x44 =L= 8;
e48.. exp(2.99573227355399 - x55)*x20 + exp(1.38629436111989 - x56)*x45 =L= 8;
e49.. exp(2.99573227355399 - x55)*x21 + exp(1.38629436111989 - x56)*x46 =L= 8;
e50.. exp(2.99573227355399 - x55)*x22 + exp(1.38629436111989 - x56)*x47 =L= 8;
e51.. exp(2.99573227355399 - x55)*x23 + exp(1.38629436111989 - x56)*x48 =L= 8;
e52.. exp(2.99573227355399 - x55)*x24 + exp(1.38629436111989 - x56)*x49 =L= 8;
e53.. exp(2.99573227355399 - x55)*x25 + exp(1.38629436111989 - x56)*x50 =L= 8;
e54.. exp(2.99573227355399 - x55)*x26 + exp(1.38629436111989 - x56)*x51 =L= 8;
e55.. exp(2.99573227355399 - x55)*x27 + exp(1.38629436111989 - x56)*x52 =L= 8;
e56.. exp(2.99573227355399 - x55)*x28 + exp(1.38629436111989 - x56)*x53 =L= 8;
e57.. exp(2.99573227355399 - x55)*x29 + exp(1.38629436111989 - x56)*x54 =L= 8;
e58.. exp(2.07944154167984 - x55)*x5 + exp(1.38629436111989 - x56)*x30 =L= 8;
e59.. exp(2.07944154167984 - x55)*x6 + exp(1.38629436111989 - x56)*x31 =L= 8;
e60.. exp(2.07944154167984 - x55)*x7 + exp(1.38629436111989 - x56)*x32 =L= 8;
e61.. exp(2.07944154167984 - x55)*x8 + exp(1.38629436111989 - x56)*x33 =L= 8;
e62.. exp(2.07944154167984 - x55)*x9 + exp(1.38629436111989 - x56)*x34 =L= 8;
e63.. exp(2.07944154167984 - x55)*x10 + exp(1.38629436111989 - x56)*x35 =L= 8;
e64.. exp(2.07944154167984 - x55)*x11 + exp(1.38629436111989 - x56)*x36 =L= 8;
e65.. exp(2.07944154167984 - x55)*x12 + exp(1.38629436111989 - x56)*x37 =L= 8;
e66.. exp(2.07944154167984 - x55)*x13 + exp(1.38629436111989 - x56)*x38 =L= 8;
e67.. exp(2.07944154167984 - x55)*x14 + exp(1.38629436111989 - x56)*x39 =L= 8;
e68.. exp(2.07944154167984 - x55)*x15 + exp(1.38629436111989 - x56)*x40 =L= 8;
e69.. exp(2.07944154167984 - x55)*x16 + exp(1.38629436111989 - x56)*x41 =L= 8;
e70.. exp(2.07944154167984 - x55)*x17 + exp(1.38629436111989 - x56)*x42 =L= 8;
e71.. exp(2.07944154167984 - x55)*x18 + exp(1.38629436111989 - x56)*x43 =L= 8;
e72.. exp(2.07944154167984 - x55)*x19 + exp(1.38629436111989 - x56)*x44 =L= 8;
e73.. exp(2.07944154167984 - x55)*x20 + exp(1.38629436111989 - x56)*x45 =L= 8;
e74.. exp(2.07944154167984 - x55)*x21 + exp(1.38629436111989 - x56)*x46 =L= 8;
e75.. exp(2.07944154167984 - x55)*x22 + exp(1.38629436111989 - x56)*x47 =L= 8;
e76.. exp(2.07944154167984 - x55)*x23 + exp(1.38629436111989 - x56)*x48 =L= 8;
e77.. exp(2.07944154167984 - x55)*x24 + exp(1.38629436111989 - x56)*x49 =L= 8;
e78.. exp(2.07944154167984 - x55)*x25 + exp(1.38629436111989 - x56)*x50 =L= 8;
e79.. exp(2.07944154167984 - x55)*x26 + exp(1.38629436111989 - x56)*x51 =L= 8;
e80.. exp(2.07944154167984 - x55)*x27 + exp(1.38629436111989 - x56)*x52 =L= 8;
e81.. exp(2.07944154167984 - x55)*x28 + exp(1.38629436111989 - x56)*x53 =L= 8;
e82.. exp(2.07944154167984 - x55)*x29 + exp(1.38629436111989 - x56)*x54 =L= 8;
* 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 = 4.82831; x55.up = 7.1591;
x56.lo = 4.42285; x56.up = 6.7071;
* set non-default levels
x2.l = 6.21460809842219;
x3.l = 6.21460809842219;
x4.l = 6.21460809842219;
x5.l = 160;
x6.l = 160;
x7.l = 160;
x8.l = 160;
x9.l = 160;
x10.l = 160;
x11.l = 160;
x12.l = 160;
x13.l = 160;
x14.l = 160;
x15.l = 160;
x16.l = 160;
x17.l = 160;
x18.l = 160;
x19.l = 160;
x20.l = 160;
x21.l = 160;
x22.l = 160;
x23.l = 160;
x24.l = 160;
x25.l = 160;
x26.l = 160;
x27.l = 160;
x28.l = 160;
x29.l = 160;
x30.l = 60;
x31.l = 60;
x32.l = 60;
x33.l = 60;
x34.l = 60;
x35.l = 60;
x36.l = 60;
x37.l = 60;
x38.l = 60;
x39.l = 60;
x40.l = 60;
x41.l = 60;
x42.l = 60;
x43.l = 60;
x44.l = 60;
x45.l = 60;
x46.l = 60;
x47.l = 60;
x48.l = 60;
x49.l = 60;
x50.l = 60;
x51.l = 60;
x52.l = 60;
x53.l = 60;
x54.l = 60;
x55.l = 4.82831;
x56.l = 4.42285;
Model m / all /;
m.limrow=0; m.limcol=0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2024-08-26 Git hash: 6cc1607f