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Instance: ex8_2_4b

Formats ams gms mod nl osil
Primal Bounds
-1197.13189900 p1 ( gdx sol )
(infeas: 7e-15)
Dual Bounds
-1197.13190300 (ANTIGONE)
-1197.13190100 (BARON)
-1197.13190000 (COUENNE)
-1197.13205700 (LINDO)
-1376.97016700 (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.
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 and common multiplicative sub-expression exp(data-b(i)) replaced
Added to library 31 Jul 2001
Problem type NLP
#Variables 61
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 61
#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 87
#Linear Constraints 6
#Quadratic Constraints 75
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 6
Operands in Gen. Nonlin. Functions exp
Constraints curvature indefinite
#Nonzeros in Jacobian 324
#Nonlinear Nonzeros in Jacobian 306
#Nonzeros in (Upper-Left) Hessian of Lagrangian 305
#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 28
Average blocksize in Hessian of Lagrangian 8.714286
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0.1724
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         88        7        6       75        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         62       62        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        378       69      309        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,x59,x60,x61,x62;

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,e83,e84,e85,e86,e87
          ,e88;


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*x60 =L= 8;

e9.. x6*x57 + x31*x60 =L= 8;

e10.. x7*x57 + x32*x60 =L= 8;

e11.. x8*x57 + x33*x60 =L= 8;

e12.. x9*x57 + x34*x60 =L= 8;

e13.. x10*x57 + x35*x60 =L= 8;

e14.. x11*x57 + x36*x60 =L= 8;

e15.. x12*x57 + x37*x60 =L= 8;

e16.. x13*x57 + x38*x60 =L= 8;

e17.. x14*x57 + x39*x60 =L= 8;

e18.. x15*x57 + x40*x60 =L= 8;

e19.. x16*x57 + x41*x60 =L= 8;

e20.. x17*x57 + x42*x60 =L= 8;

e21.. x18*x57 + x43*x60 =L= 8;

e22.. x19*x57 + x44*x60 =L= 8;

e23.. x20*x57 + x45*x60 =L= 8;

e24.. x21*x57 + x46*x60 =L= 8;

e25.. x22*x57 + x47*x60 =L= 8;

e26.. x23*x57 + x48*x60 =L= 8;

e27.. x24*x57 + x49*x60 =L= 8;

e28.. x25*x57 + x50*x60 =L= 8;

e29.. x26*x57 + x51*x60 =L= 8;

e30.. x27*x57 + x52*x60 =L= 8;

e31.. x28*x57 + x53*x60 =L= 8;

e32.. x29*x57 + x54*x60 =L= 8;

e33.. x5*x58 + x30*x61 =L= 8;

e34.. x6*x58 + x31*x61 =L= 8;

e35.. x7*x58 + x32*x61 =L= 8;

e36.. x8*x58 + x33*x61 =L= 8;

e37.. x9*x58 + x34*x61 =L= 8;

e38.. x10*x58 + x35*x61 =L= 8;

e39.. x11*x58 + x36*x61 =L= 8;

e40.. x12*x58 + x37*x61 =L= 8;

e41.. x13*x58 + x38*x61 =L= 8;

e42.. x14*x58 + x39*x61 =L= 8;

e43.. x15*x58 + x40*x61 =L= 8;

e44.. x16*x58 + x41*x61 =L= 8;

e45.. x17*x58 + x42*x61 =L= 8;

e46.. x18*x58 + x43*x61 =L= 8;

e47.. x19*x58 + x44*x61 =L= 8;

e48.. x20*x58 + x45*x61 =L= 8;

e49.. x21*x58 + x46*x61 =L= 8;

e50.. x22*x58 + x47*x61 =L= 8;

e51.. x23*x58 + x48*x61 =L= 8;

e52.. x24*x58 + x49*x61 =L= 8;

e53.. x25*x58 + x50*x61 =L= 8;

e54.. x26*x58 + x51*x61 =L= 8;

e55.. x27*x58 + x52*x61 =L= 8;

e56.. x28*x58 + x53*x61 =L= 8;

e57.. x29*x58 + x54*x61 =L= 8;

e58.. x5*x59 + x30*x62 =L= 8;

e59.. x6*x59 + x31*x62 =L= 8;

e60.. x7*x59 + x32*x62 =L= 8;

e61.. x8*x59 + x33*x62 =L= 8;

e62.. x9*x59 + x34*x62 =L= 8;

e63.. x10*x59 + x35*x62 =L= 8;

e64.. x11*x59 + x36*x62 =L= 8;

e65.. x12*x59 + x37*x62 =L= 8;

e66.. x13*x59 + x38*x62 =L= 8;

e67.. x14*x59 + x39*x62 =L= 8;

e68.. x15*x59 + x40*x62 =L= 8;

e69.. x16*x59 + x41*x62 =L= 8;

e70.. x17*x59 + x42*x62 =L= 8;

e71.. x18*x59 + x43*x62 =L= 8;

e72.. x19*x59 + x44*x62 =L= 8;

e73.. x20*x59 + x45*x62 =L= 8;

e74.. x21*x59 + x46*x62 =L= 8;

e75.. x22*x59 + x47*x62 =L= 8;

e76.. x23*x59 + x48*x62 =L= 8;

e77.. x24*x59 + x49*x62 =L= 8;

e78.. x25*x59 + x50*x62 =L= 8;

e79.. x26*x59 + x51*x62 =L= 8;

e80.. x27*x59 + x52*x62 =L= 8;

e81.. x28*x59 + x53*x62 =L= 8;

e82.. x29*x59 + x54*x62 =L= 8;

e83.. -exp(2.07944154167984 - x55) + x57 =E= 0;

e84.. -exp(2.99573227355399 - x55) + x58 =E= 0;

e85.. -exp(2.07944154167984 - x55) + x59 =E= 0;

e86.. -exp(2.77258872223978 - x56) + x60 =E= 0;

e87.. -exp(1.38629436111989 - x56) + x61 =E= 0;

e88.. -exp(1.38629436111989 - x56) + x62 =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 = 4.82831; x55.up = 7.1591;
x56.lo = 4.42285; x56.up = 6.7071;
x57.lo = 0.00622203373693604; x57.up = 0.0640002391877942;
x58.lo = 0.0155550843423401; x58.up = 0.160000597969486;
x59.lo = 0.00622203373693604; x59.up = 0.0640002391877942;
x60.lo = 0.019555254080048; x60.up = 0.191999736805455;
x61.lo = 0.00488881352001201; x61.up = 0.0479999342013636;
x62.lo = 0.00488881352001201; x62.up = 0.0479999342013636;

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: 2018-09-14 Git hash: ac5a5314
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