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Instance: ex8_3_13

Formats ams gms mod nl osil
Primal Bounds
-36.08469789 p1 ( gdx sol )
(infeas: 4e-14)
-41.91808248 p2 ( gdx sol )
(infeas: 4e-14)
-42.65345802 p3 ( gdx sol )
(infeas: 6e-14)
-43.08947815 p4 ( gdx sol )
(infeas: 7e-13)
Dual Bounds
-49.93994239 (ANTIGONE)
-43.08947820 (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 ex8.3.13 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 115
#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 6
#Nonlinear Nonzeros in Objective 0
#Constraints 72
#Linear Constraints 18
#Quadratic Constraints 44
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 10
Operands in Gen. Nonlin. Functions mul div vcpower exp
Constraints curvature indefinite
#Nonzeros in Jacobian 569
#Nonlinear Nonzeros in Jacobian 448
#Nonzeros in (Upper-Left) Hessian of Lagrangian 393
#Nonzeros in Diagonal of Hessian of Lagrangian 15
#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
Infeasibility of initial point 300
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
*         73       73        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        116      116        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        576      128      448        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,x112,x113,x114,x115
          ,x116;

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,x97,x98,x99,x100,x101
          ,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116;

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;


e1..  - objvar - 100*x95 + x97 + x98 + x99 + x100 + x101 =E= 0;

e2..  - x2 - x3 - x4 - x5 - x6 =E= -50;

e3..  - x7 - x8 - x9 - x10 - x11 =E= -50;

e4..  - x2 - x7 + x12 - x62 - x67 - x72 - x77 - x82 =E= 0;

e5..  - x3 - x8 + x13 - x63 - x68 - x73 - x78 - x83 =E= 0;

e6..  - x4 - x9 + x14 - x64 - x69 - x74 - x79 - x84 =E= 0;

e7..  - x5 - x10 + x15 - x65 - x70 - x75 - x80 - x85 =E= 0;

e8..  - x6 - x11 + x16 - x66 - x71 - x76 - x81 - x86 =E= 0;

e9.. x17*x12 - (x42*x62 + x46*x67 + x50*x72 + x54*x77 + x58*x82) - x2 =E= 0;

e10.. x18*x12 - (x43*x62 + x47*x67 + x51*x72 + x55*x77 + x59*x82) - x7 =E= 0;

e11.. x19*x12 - (x44*x62 + x48*x67 + x52*x72 + x56*x77 + x60*x82) =E= 0;

e12.. x20*x12 - (x45*x62 + x49*x67 + x53*x72 + x57*x77 + x61*x82) =E= 0;

e13.. x21*x13 - (x42*x63 + x46*x68 + x50*x73 + x54*x78 + x58*x83) - x3 =E= 0;

e14.. x22*x13 - (x43*x63 + x47*x68 + x51*x73 + x55*x78 + x59*x83) - x8 =E= 0;

e15.. x23*x13 - (x44*x63 + x48*x68 + x52*x73 + x56*x78 + x60*x83) =E= 0;

e16.. x24*x13 - (x45*x63 + x49*x68 + x53*x73 + x57*x78 + x61*x83) =E= 0;

e17.. x25*x14 - (x42*x64 + x46*x69 + x50*x74 + x54*x79 + x58*x84) - x4 =E= 0;

e18.. x26*x14 - (x43*x64 + x47*x69 + x51*x74 + x55*x79 + x59*x84) - x9 =E= 0;

e19.. x27*x14 - (x44*x64 + x48*x69 + x52*x74 + x56*x79 + x60*x84) =E= 0;

e20.. x28*x14 - (x45*x64 + x49*x69 + x53*x74 + x57*x79 + x61*x84) =E= 0;

e21.. x29*x15 - (x42*x65 + x46*x70 + x50*x75 + x54*x80 + x58*x85) - x5 =E= 0;

e22.. x30*x15 - (x43*x65 + x47*x70 + x51*x75 + x55*x80 + x59*x85) - x10 =E= 0;

e23.. x31*x15 - (x44*x65 + x48*x70 + x52*x75 + x56*x80 + x60*x85) =E= 0;

e24.. x32*x15 - (x45*x65 + x49*x70 + x53*x75 + x57*x80 + x61*x85) =E= 0;

e25.. x33*x16 - (x42*x66 + x46*x71 + x50*x76 + x54*x81 + x58*x86) - x6 =E= 0;

e26.. x34*x16 - (x43*x66 + x47*x71 + x51*x76 + x55*x81 + x59*x86) - x11 =E= 0;

e27.. x35*x16 - (x44*x66 + x48*x71 + x52*x76 + x56*x81 + x60*x86) =E= 0;

e28.. x36*x16 - (x45*x66 + x49*x71 + x53*x76 + x57*x81 + x61*x86) =E= 0;

e29..  - x12 + x37 =E= 0;

e30..  - x13 + x38 =E= 0;

e31..  - x14 + x39 =E= 0;

e32..  - x15 + x40 =E= 0;

e33..  - x16 + x41 =E= 0;

e34.. x42*x37 - (x17*x12 + x97*(-x107 - x108)) =E= 0;

e35.. x43*x37 - (x18*x12 + x97*(-x107 - x108)) =E= 0;

e36.. x44*x37 - (x19*x12 + x97*x107) =E= 0;

e37.. x45*x37 - (x20*x12 + x97*x108) =E= 0;

e38.. x46*x38 - (x21*x13 + x98*(-x109 - x110)) =E= 0;

e39.. x47*x38 - (x22*x13 + x98*(-x109 - x110)) =E= 0;

e40.. x48*x38 - (x23*x13 + x98*x109) =E= 0;

e41.. x49*x38 - (x24*x13 + x98*x110) =E= 0;

e42.. x50*x39 - (x25*x14 + x99*(-x111 - x112)) =E= 0;

e43.. x51*x39 - (x26*x14 + x99*(-x111 - x112)) =E= 0;

e44.. x52*x39 - (x27*x14 + x99*x111) =E= 0;

e45.. x53*x39 - (x28*x14 + x99*x112) =E= 0;

e46.. x54*x40 - (x29*x15 + x100*(-x113 - x114)) =E= 0;

e47.. x55*x40 - (x30*x15 + x100*(-x113 - x114)) =E= 0;

e48.. x56*x40 - (x31*x15 + x100*x113) =E= 0;

e49.. x57*x40 - (x32*x15 + x100*x114) =E= 0;

e50.. x58*x41 - (x33*x16 + x101*(-x115 - x116)) =E= 0;

e51.. x59*x41 - (x34*x16 + x101*(-x115 - x116)) =E= 0;

e52.. x60*x41 - (x35*x16 + x101*x115) =E= 0;

e53.. x61*x41 - (x36*x16 + x101*x116) =E= 0;

e54.. -54000000*exp(-9631.60543532964/x102)*x42*x43**0.3 + x107 =E= 0;

e55.. -54000000*exp(-9631.60543532964/x103)*x46*x47**0.3 + x109 =E= 0;

e56.. -54000000*exp(-9631.60543532964/x104)*x50*x51**0.3 + x111 =E= 0;

e57.. -54000000*exp(-9631.60543532964/x105)*x54*x55**0.3 + x113 =E= 0;

e58.. -54000000*exp(-9631.60543532964/x106)*x58*x59**0.3 + x115 =E= 0;

e59.. -360000*exp(-4815.80271766482/x102)*x42**0.5*x43**1.8 + x108 =E= 0;

e60.. -360000*exp(-4815.80271766482/x103)*x46**0.5*x47**1.8 + x110 =E= 0;

e61.. -360000*exp(-4815.80271766482/x104)*x50**0.5*x51**1.8 + x112 =E= 0;

e62.. -360000*exp(-4815.80271766482/x105)*x54**0.5*x55**1.8 + x114 =E= 0;

e63.. -360000*exp(-4815.80271766482/x106)*x58**0.5*x59**1.8 + x116 =E= 0;

e64..    x37 - x62 - x63 - x64 - x65 - x66 - x87 =E= 0;

e65..    x38 - x67 - x68 - x69 - x70 - x71 - x88 =E= 0;

e66..    x39 - x72 - x73 - x74 - x75 - x76 - x89 =E= 0;

e67..    x40 - x77 - x78 - x79 - x80 - x81 - x90 =E= 0;

e68..    x41 - x82 - x83 - x84 - x85 - x86 - x91 =E= 0;

e69..  - x87 - x88 - x89 - x90 - x91 + x92 =E= 0;

e70.. x92*x93 - (x87*x42 + x88*x46 + x89*x50 + x90*x54 + x91*x58) =E= 0;

e71.. x92*x94 - (x87*x43 + x88*x47 + x89*x51 + x90*x55 + x91*x59) =E= 0;

e72.. x92*x95 - (x87*x44 + x88*x48 + x89*x52 + x90*x56 + x91*x60) =E= 0;

e73.. x92*x96 - (x87*x45 + x88*x49 + x89*x53 + x90*x57 + x91*x61) =E= 0;

* set non-default bounds
x2.up = 1000;
x3.up = 1000;
x4.up = 1000;
x5.up = 1000;
x6.up = 1000;
x7.up = 1000;
x8.up = 1000;
x9.up = 1000;
x10.up = 1000;
x11.up = 1000;
x12.up = 1000;
x13.up = 1000;
x14.up = 1000;
x15.up = 1000;
x16.up = 1000;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1000;
x38.up = 1000;
x39.up = 1000;
x40.up = 1000;
x41.up = 1000;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1000;
x63.up = 1000;
x64.up = 1000;
x65.up = 1000;
x66.up = 1000;
x67.up = 1000;
x68.up = 1000;
x69.up = 1000;
x70.up = 1000;
x71.up = 1000;
x72.up = 1000;
x73.up = 1000;
x74.up = 1000;
x75.up = 1000;
x76.up = 1000;
x77.up = 1000;
x78.up = 1000;
x79.up = 1000;
x80.up = 1000;
x81.up = 1000;
x82.up = 1000;
x83.up = 1000;
x84.up = 1000;
x85.up = 1000;
x86.up = 1000;
x87.up = 1000;
x88.up = 1000;
x89.up = 1000;
x90.up = 1000;
x91.up = 1000;
x92.up = 1000;
x93.up = 1;
x94.up = 1;
x95.up = 1;
x96.up = 1;
x97.up = 10000;
x98.up = 10000;
x99.up = 10000;
x100.up = 10000;
x101.up = 10000;
x102.lo = 300; x102.up = 800;
x103.lo = 300; x103.up = 800;
x104.lo = 300; x104.up = 800;
x105.lo = 300; x105.up = 800;
x106.lo = 300; x106.up = 800;
x107.up = 10000;
x108.up = 10000;
x109.up = 10000;
x110.up = 10000;
x111.up = 10000;
x112.up = 10000;
x113.up = 10000;
x114.up = 10000;
x115.up = 10000;
x116.up = 10000;

* set non-default levels
x2.l = 50;
x3.l = 50;
x4.l = 50;
x5.l = 50;
x6.l = 50;
x7.l = 50;
x8.l = 50;
x9.l = 50;
x10.l = 50;
x11.l = 50;
x12.l = 50;
x13.l = 50;
x14.l = 50;
x15.l = 50;
x16.l = 50;
x17.l = 0.2;
x18.l = 0.2;
x19.l = 0.2;
x20.l = 0.2;
x21.l = 0.2;
x22.l = 0.2;
x23.l = 0.2;
x24.l = 0.2;
x25.l = 0.2;
x26.l = 0.2;
x27.l = 0.2;
x28.l = 0.2;
x29.l = 0.2;
x30.l = 0.2;
x31.l = 0.2;
x32.l = 0.2;
x33.l = 0.2;
x34.l = 0.2;
x35.l = 0.2;
x36.l = 0.2;
x37.l = 100;
x38.l = 100;
x39.l = 100;
x40.l = 100;
x41.l = 100;
x42.l = 0.2;
x43.l = 0.2;
x44.l = 0.2;
x45.l = 0.2;
x46.l = 0.2;
x47.l = 0.2;
x48.l = 0.2;
x49.l = 0.2;
x50.l = 0.2;
x51.l = 0.2;
x52.l = 0.2;
x53.l = 0.2;
x54.l = 0.2;
x55.l = 0.2;
x56.l = 0.2;
x57.l = 0.2;
x58.l = 0.2;
x59.l = 0.2;
x60.l = 0.2;
x61.l = 0.2;
x62.l = 50;
x63.l = 50;
x64.l = 50;
x65.l = 50;
x66.l = 50;
x67.l = 50;
x68.l = 50;
x69.l = 50;
x70.l = 50;
x71.l = 50;
x72.l = 50;
x73.l = 50;
x74.l = 50;
x75.l = 50;
x76.l = 50;
x77.l = 50;
x78.l = 50;
x79.l = 50;
x80.l = 50;
x81.l = 50;
x82.l = 50;
x83.l = 50;
x84.l = 50;
x85.l = 50;
x86.l = 50;
x87.l = 50;
x88.l = 50;
x89.l = 50;
x90.l = 50;
x91.l = 50;
x92.l = 100;
x93.l = 0.2;
x94.l = 0.2;
x95.l = 0.2;
x96.l = 0.2;
x97.l = 1;
x98.l = 1;
x99.l = 1;
x100.l = 1;
x101.l = 1;
x102.l = 400;
x103.l = 400;
x104.l = 400;
x105.l = 400;
x106.l = 400;

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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