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Removed Instance ex8_3_14

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
-2.49863871 p1 ( gdx sol )
(infeas: 6e-11)
Other points (infeas > 1e-08)  
Dual Bounds
-2.49863871 (ANTIGONE)
-100.00000000 (BARON)
-100.00000000 (COUENNE)
-100.00000000 (LINDO)
-100.00000000 (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.
Schweiger, C A and Floudas, C A, Optimization Framework for the Synthesis of Chemical Reactor Networks, Industrial and Engineering Chemistry Research, 38:3, 1998, 744-766.
Source Test Problem ex8.3.14 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Removed from library 01 Mar 2022
Removed because Numerically difficult formulation (coefficient of order 1E16 in front of exp())
Problem type NLP
#Variables 110
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 105
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 71
#Linear Constraints 17
#Quadratic Constraints 44
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 10
Operands in Gen. Nonlin. Functions div exp mul vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 579
#Nonlinear Nonzeros in Jacobian 463
#Nonzeros in (Upper-Left) Hessian of Lagrangian 473
#Nonzeros in Diagonal of Hessian of Lagrangian 25
#Blocks in Hessian of Lagrangian 16
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 12
Average blocksize in Hessian of Lagrangian 6.5625
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.0000e-01
Maximal coefficient 2.7320e+16
Infeasibility of initial point 1.366e+06
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
*         72       72        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        111      111        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        581      118      463        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,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111;

Positive Variables  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,x63,x64,x65,x66,x67,x68
          ,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85
          ,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x102,x103,x104,x105
          ,x106,x107,x108,x109,x110,x111;

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;


e1..  - objvar - x90 =E= 0;

e2..  - x2 - x3 - x4 - x5 - x6 =E= -7731;

e3..  - x2 + x7 - x57 - x62 - x67 - x72 - x77 =E= 0;

e4..  - x3 + x8 - x58 - x63 - x68 - x73 - x78 =E= 0;

e5..  - x4 + x9 - x59 - x64 - x69 - x74 - x79 =E= 0;

e6..  - x5 + x10 - x60 - x65 - x70 - x75 - x80 =E= 0;

e7..  - x6 + x11 - x61 - x66 - x71 - x76 - x81 =E= 0;

e8.. x12*x7 - (x37*x57 + x41*x62 + x45*x67 + x49*x72 + x53*x77) - 2.5*x2 =E= 0;

e9.. x13*x7 - (x38*x57 + x42*x62 + x46*x67 + x50*x72 + x54*x77) - 3.46*x2 =E= 0
     ;

e10.. x14*x7 - (x39*x57 + x43*x62 + x47*x67 + x51*x72 + x55*x77) =E= 0;

e11.. x15*x7 - (x40*x57 + x44*x62 + x48*x67 + x52*x72 + x56*x77) - 26.05*x2
       =E= 0;

e12.. x16*x8 - (x37*x58 + x41*x63 + x45*x68 + x49*x73 + x53*x78) - 2.5*x3 =E= 0
      ;

e13.. x17*x8 - (x38*x58 + x42*x63 + x46*x68 + x50*x73 + x54*x78) - 3.46*x3
       =E= 0;

e14.. x18*x8 - (x39*x58 + x43*x63 + x47*x68 + x51*x73 + x55*x78) =E= 0;

e15.. x19*x8 - (x40*x58 + x44*x63 + x48*x68 + x52*x73 + x56*x78) - 26.05*x3
       =E= 0;

e16.. x20*x9 - (x37*x59 + x41*x64 + x45*x69 + x49*x74 + x53*x79) - 2.5*x4 =E= 0
      ;

e17.. x21*x9 - (x38*x59 + x42*x64 + x46*x69 + x50*x74 + x54*x79) - 3.46*x4
       =E= 0;

e18.. x22*x9 - (x39*x59 + x43*x64 + x47*x69 + x51*x74 + x55*x79) =E= 0;

e19.. x23*x9 - (x40*x59 + x44*x64 + x48*x69 + x52*x74 + x56*x79) - 26.05*x4
       =E= 0;

e20.. x24*x10 - (x37*x60 + x41*x65 + x45*x70 + x49*x75 + x53*x80) - 2.5*x5
       =E= 0;

e21.. x25*x10 - (x38*x60 + x42*x65 + x46*x70 + x50*x75 + x54*x80) - 3.46*x5
       =E= 0;

e22.. x26*x10 - (x39*x60 + x43*x65 + x47*x70 + x51*x75 + x55*x80) =E= 0;

e23.. x27*x10 - (x40*x60 + x44*x65 + x48*x70 + x52*x75 + x56*x80) - 26.05*x5
       =E= 0;

e24.. x28*x11 - (x37*x61 + x41*x66 + x45*x71 + x49*x76 + x53*x81) - 2.5*x6
       =E= 0;

e25.. x29*x11 - (x38*x61 + x42*x66 + x46*x71 + x50*x76 + x54*x81) - 3.46*x6
       =E= 0;

e26.. x30*x11 - (x39*x61 + x43*x66 + x47*x71 + x51*x76 + x55*x81) =E= 0;

e27.. x31*x11 - (x40*x61 + x44*x66 + x48*x71 + x52*x76 + x56*x81) - 26.05*x6
       =E= 0;

e28..  - x7 + x32 =E= 0;

e29..  - x8 + x33 =E= 0;

e30..  - x9 + x34 =E= 0;

e31..  - x10 + x35 =E= 0;

e32..  - x11 + x36 =E= 0;

e33.. x37*x32 - (x12*x7 + x92*(x103 - x102)) =E= 0;

e34.. x38*x32 - (x13*x7 + x92*(0.5*x103 - 0.5*x102)) =E= 0;

e35.. x39*x32 - (x14*x7 + x92*(x102 - x103)) =E= 0;

e36.. x40*x32 - x15*x7 =E= 0;

e37.. x41*x33 - (x16*x8 + x93*(x105 - x104)) =E= 0;

e38.. x42*x33 - (x17*x8 + x93*(0.5*x105 - 0.5*x104)) =E= 0;

e39.. x43*x33 - (x18*x8 + x93*(x104 - x105)) =E= 0;

e40.. x44*x33 - x19*x8 =E= 0;

e41.. x45*x34 - (x20*x9 + x94*(x107 - x106)) =E= 0;

e42.. x46*x34 - (x21*x9 + x94*(0.5*x107 - 0.5*x106)) =E= 0;

e43.. x47*x34 - (x22*x9 + x94*(x106 - x107)) =E= 0;

e44.. x48*x34 - x23*x9 =E= 0;

e45.. x49*x35 - (x24*x10 + x95*(x109 - x108)) =E= 0;

e46.. x50*x35 - (x25*x10 + x95*(0.5*x109 - 0.5*x108)) =E= 0;

e47.. x51*x35 - (x26*x10 + x95*(x108 - x109)) =E= 0;

e48.. x52*x35 - x27*x10 =E= 0;

e49.. x53*x36 - (x28*x11 + x96*(x111 - x110)) =E= 0;

e50.. x54*x36 - (x29*x11 + x96*(0.5*x111 - 0.5*x110)) =E= 0;

e51.. x55*x36 - (x30*x11 + x96*(x110 - x111)) =E= 0;

e52.. x56*x36 - x31*x11 =E= 0;

e53.. -628400000000*exp(-15500/x97)*x37**0.5*x38/(x37 + x38 + x39 + x40)**1.5
       + x102 =E= 0;

e54.. -628400000000*exp(-15500/x98)*x41**0.5*x42/(x41 + x42 + x43 + x44)**1.5
       + x104 =E= 0;

e55.. -628400000000*exp(-15500/x99)*x45**0.5*x46/(x45 + x46 + x47 + x48)**1.5
       + x106 =E= 0;

e56.. -628400000000*exp(-15500/x100)*x49**0.5*x50/(x49 + x50 + x51 + x52)**1.5
       + x108 =E= 0;

e57.. -628400000000*exp(-15500/x101)*x53**0.5*x54/(x53 + x54 + x55 + x56)**1.5
       + x110 =E= 0;

e58.. -2.732e16*exp(-26799.5/x97)*x38**0.5*x39/x37**0.5/(x37 + x38 + x39 + x40)
       + x103 =E= 0;

e59.. -2.732e16*exp(-26799.5/x98)*x42**0.5*x43/x41**0.5/(x41 + x42 + x43 + x44)
       + x105 =E= 0;

e60.. -2.732e16*exp(-26799.5/x99)*x46**0.5*x47/x45**0.5/(x45 + x46 + x47 + x48)
       + x107 =E= 0;

e61.. -2.732e16*exp(-26799.5/x100)*x50**0.5*x51/x49**0.5/(x49 + x50 + x51 + x52
      ) + x109 =E= 0;

e62.. -2.732e16*exp(-26799.5/x101)*x54**0.5*x55/x53**0.5/(x53 + x54 + x55 + x56
      ) + x111 =E= 0;

e63..    x32 - x57 - x58 - x59 - x60 - x61 - x82 =E= 0;

e64..    x33 - x62 - x63 - x64 - x65 - x66 - x83 =E= 0;

e65..    x34 - x67 - x68 - x69 - x70 - x71 - x84 =E= 0;

e66..    x35 - x72 - x73 - x74 - x75 - x76 - x85 =E= 0;

e67..    x36 - x77 - x78 - x79 - x80 - x81 - x86 =E= 0;

e68..  - x82 - x83 - x84 - x85 - x86 + x87 =E= 0;

e69.. x87*x88 - (x82*x37 + x83*x41 + x84*x45 + x85*x49 + x86*x53) =E= 0;

e70.. x87*x89 - (x82*x38 + x83*x42 + x84*x46 + x85*x50 + x86*x54) =E= 0;

e71.. x87*x90 - (x82*x39 + x83*x43 + x84*x47 + x85*x51 + x86*x55) =E= 0;

e72.. x87*x91 - (x82*x40 + x83*x44 + x84*x48 + x85*x52 + x86*x56) =E= 0;

* set non-default bounds
x2.up = 10000;
x3.up = 10000;
x4.up = 10000;
x5.up = 10000;
x6.up = 10000;
x7.up = 10000;
x8.up = 10000;
x9.up = 10000;
x10.up = 10000;
x11.up = 10000;
x12.up = 100;
x13.up = 100;
x14.up = 100;
x15.up = 100;
x16.up = 100;
x17.up = 100;
x18.up = 100;
x19.up = 100;
x20.up = 100;
x21.up = 100;
x22.up = 100;
x23.up = 100;
x24.up = 100;
x25.up = 100;
x26.up = 100;
x27.up = 100;
x28.up = 100;
x29.up = 100;
x30.up = 100;
x31.up = 100;
x32.up = 10000;
x33.up = 10000;
x34.up = 10000;
x35.up = 10000;
x36.up = 10000;
x37.up = 100;
x38.up = 100;
x39.up = 100;
x40.up = 100;
x41.up = 100;
x42.up = 100;
x43.up = 100;
x44.up = 100;
x45.up = 100;
x46.up = 100;
x47.up = 100;
x48.up = 100;
x49.up = 100;
x50.up = 100;
x51.up = 100;
x52.up = 100;
x53.up = 100;
x54.up = 100;
x55.up = 100;
x56.up = 100;
x57.up = 10000;
x58.up = 10000;
x59.up = 10000;
x60.up = 10000;
x61.up = 10000;
x62.up = 10000;
x63.up = 10000;
x64.up = 10000;
x65.up = 10000;
x66.up = 10000;
x67.up = 10000;
x68.up = 10000;
x69.up = 10000;
x70.up = 10000;
x71.up = 10000;
x72.up = 10000;
x73.up = 10000;
x74.up = 10000;
x75.up = 10000;
x76.up = 10000;
x77.up = 10000;
x78.up = 10000;
x79.up = 10000;
x80.up = 10000;
x81.up = 10000;
x82.up = 10000;
x83.up = 10000;
x84.up = 10000;
x85.up = 10000;
x86.up = 10000;
x87.up = 10000;
x88.up = 100;
x89.up = 100;
x90.up = 100;
x91.up = 100;
x92.up = 50000;
x93.up = 50000;
x94.up = 50000;
x95.up = 50000;
x96.up = 50000;
x97.lo = 300; x97.up = 1200;
x98.lo = 300; x98.up = 1200;
x99.lo = 300; x99.up = 1200;
x100.lo = 300; x100.up = 1200;
x101.lo = 300; x101.up = 1200;
x102.up = 100000;
x103.up = 100000;
x104.up = 100000;
x105.up = 100000;
x106.up = 100000;
x107.up = 100000;
x108.up = 100000;
x109.up = 100000;
x110.up = 100000;
x111.up = 100000;

* set non-default levels
x2.l = 7731;
x3.l = 7731;
x4.l = 7731;
x5.l = 7731;
x6.l = 7731;
x7.l = 7731;
x8.l = 7731;
x9.l = 7731;
x10.l = 7731;
x11.l = 7731;
x12.l = 1;
x13.l = 1;
x14.l = 1;
x15.l = 1;
x16.l = 1;
x17.l = 1;
x18.l = 1;
x19.l = 1;
x20.l = 1;
x21.l = 1;
x22.l = 1;
x23.l = 1;
x24.l = 1;
x25.l = 1;
x26.l = 1;
x27.l = 1;
x28.l = 1;
x29.l = 1;
x30.l = 1;
x31.l = 1;
x32.l = 7731;
x33.l = 7731;
x34.l = 7731;
x35.l = 7731;
x36.l = 7731;
x37.l = 1;
x38.l = 1;
x39.l = 1;
x40.l = 1;
x41.l = 1;
x42.l = 1;
x43.l = 1;
x44.l = 1;
x45.l = 1;
x46.l = 1;
x47.l = 1;
x48.l = 1;
x49.l = 1;
x50.l = 1;
x51.l = 1;
x52.l = 1;
x53.l = 1;
x54.l = 1;
x55.l = 1;
x56.l = 1;
x57.l = 7731;
x58.l = 7731;
x59.l = 7731;
x60.l = 7731;
x61.l = 7731;
x62.l = 7731;
x63.l = 7731;
x64.l = 7731;
x65.l = 7731;
x66.l = 7731;
x67.l = 7731;
x68.l = 7731;
x69.l = 7731;
x70.l = 7731;
x71.l = 7731;
x72.l = 7731;
x73.l = 7731;
x74.l = 7731;
x75.l = 7731;
x76.l = 7731;
x77.l = 7731;
x78.l = 7731;
x79.l = 7731;
x80.l = 7731;
x81.l = 7731;
x82.l = 7731;
x83.l = 7731;
x84.l = 7731;
x85.l = 7731;
x86.l = 7731;
x87.l = 7731;
x88.l = 1;
x89.l = 1;
x90.l = 1;
x91.l = 1;
x92.l = 1;
x93.l = 1;
x94.l = 1;
x95.l = 1;
x96.l = 1;
x97.l = 1200;
x98.l = 1200;
x99.l = 1200;
x100.l = 1200;
x101.l = 1200;

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: 2022-06-23 Git hash: c4ba8ecd
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