MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Removed Instance ex8_3_12

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
-0.00000000 p1 ( gdx sol )
(infeas: 1e-11)
-0.99270440 p2 ( gdx sol )
(infeas: 1e-13)
-0.99380220 p3 ( gdx sol )
(infeas: 6e-14)
Other points (infeas > 1e-08)  
Dual Bounds
-0.99380220 (ANTIGONE)
-10.00000000 (BARON)
-10.00000000 (COUENNE)
-10.00000000 (LINDO)
-10.00000000 (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 ex8.3.12 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 1E17 in front of exp())
Problem type NLP
#Variables 120
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 115
#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 81
#Linear Constraints 17
#Quadratic Constraints 44
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 20
Operands in Gen. Nonlin. Functions div exp mul
Constraints curvature indefinite
#Nonzeros in Jacobian 584
#Nonlinear Nonzeros in Jacobian 468
#Nonzeros in (Upper-Left) Hessian of Lagrangian 403
#Nonzeros in Diagonal of Hessian of Lagrangian 5
#Blocks in Hessian of Lagrangian 16
Minimal blocksize in Hessian of Lagrangian 5
Maximal blocksize in Hessian of Lagrangian 12
Average blocksize in Hessian of Lagrangian 7.1875
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 8.1500e+17
Infeasibility of initial point 250
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
*         82       82        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        121      121        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        586      118      468        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,x117,x118,x119,x120,x121;

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,x112,x113,x114,x115,x116,x117,x118
          ,x119,x120,x121;

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..  - objvar - x90 =E= 0;

e2..  - x2 - x3 - x4 - x5 - x6 =E= -100;

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) - x2 =E= 0;

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

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

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

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

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

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

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

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

e25.. x29*x11 - (x38*x61 + x42*x66 + x46*x71 + x50*x76 + x54*x81) =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) =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*(-x102 - x103)) =E= 0;

e34.. x38*x32 - (x13*x7 + x92*(x102 - x104)) =E= 0;

e35.. x39*x32 - (x14*x7 + x92*(x103 + x104 - x105)) =E= 0;

e36.. x40*x32 - (x15*x7 + x92*x105) =E= 0;

e37.. x41*x33 - (x16*x8 + x93*(-x106 - x107)) =E= 0;

e38.. x42*x33 - (x17*x8 + x93*(x106 - x108)) =E= 0;

e39.. x43*x33 - (x18*x8 + x93*(x107 + x108 - x109)) =E= 0;

e40.. x44*x33 - (x19*x8 + x93*x109) =E= 0;

e41.. x45*x34 - (x20*x9 + x94*(-x110 - x111)) =E= 0;

e42.. x46*x34 - (x21*x9 + x94*(x110 - x112)) =E= 0;

e43.. x47*x34 - (x22*x9 + x94*(x111 + x112 - x113)) =E= 0;

e44.. x48*x34 - (x23*x9 + x94*x113) =E= 0;

e45.. x49*x35 - (x24*x10 + x95*(-x114 - x115)) =E= 0;

e46.. x50*x35 - (x25*x10 + x95*(x114 - x116)) =E= 0;

e47.. x51*x35 - (x26*x10 + x95*(x115 + x116 - x117)) =E= 0;

e48.. x52*x35 - (x27*x10 + x95*x117) =E= 0;

e49.. x53*x36 - (x28*x11 + x96*(-x118 - x119)) =E= 0;

e50.. x54*x36 - (x29*x11 + x96*(x118 - x120)) =E= 0;

e51.. x55*x36 - (x30*x11 + x96*(x119 + x120 - x121)) =E= 0;

e52.. x56*x36 - (x31*x11 + x96*x121) =E= 0;

e53.. -20000000000000*exp(-19124.3080020131/x97)*x37 + x102 =E= 0;

e54.. -20000000000000*exp(-19124.3080020131/x98)*x41 + x106 =E= 0;

e55.. -20000000000000*exp(-19124.3080020131/x99)*x45 + x110 =E= 0;

e56.. -20000000000000*exp(-19124.3080020131/x100)*x49 + x114 =E= 0;

e57.. -20000000000000*exp(-19124.3080020131/x101)*x53 + x118 =E= 0;

e58.. -20000000000000*exp(-19124.3080020131/x97)*x37 + x103 =E= 0;

e59.. -20000000000000*exp(-19124.3080020131/x98)*x41 + x107 =E= 0;

e60.. -20000000000000*exp(-19124.3080020131/x99)*x45 + x111 =E= 0;

e61.. -20000000000000*exp(-19124.3080020131/x100)*x49 + x115 =E= 0;

e62.. -20000000000000*exp(-19124.3080020131/x101)*x53 + x119 =E= 0;

e63.. -8.15e17*exp(-25163.5631605435/x97)*x38 + x104 =E= 0;

e64.. -8.15e17*exp(-25163.5631605435/x98)*x42 + x108 =E= 0;

e65.. -8.15e17*exp(-25163.5631605435/x99)*x46 + x112 =E= 0;

e66.. -8.15e17*exp(-25163.5631605435/x100)*x50 + x116 =E= 0;

e67.. -8.15e17*exp(-25163.5631605435/x101)*x54 + x120 =E= 0;

e68.. -210000*exp(-10065.4252642174/x97)*x39 + x105 =E= 0;

e69.. -210000*exp(-10065.4252642174/x98)*x43 + x109 =E= 0;

e70.. -210000*exp(-10065.4252642174/x99)*x47 + x113 =E= 0;

e71.. -210000*exp(-10065.4252642174/x100)*x51 + x117 =E= 0;

e72.. -210000*exp(-10065.4252642174/x101)*x55 + x121 =E= 0;

e73..    x32 - x57 - x58 - x59 - x60 - x61 - x82 =E= 0;

e74..    x33 - x62 - x63 - x64 - x65 - x66 - x83 =E= 0;

e75..    x34 - x67 - x68 - x69 - x70 - x71 - x84 =E= 0;

e76..    x35 - x72 - x73 - x74 - x75 - x76 - x85 =E= 0;

e77..    x36 - x77 - x78 - x79 - x80 - x81 - x86 =E= 0;

e78..  - x82 - x83 - x84 - x85 - x86 + x87 =E= 0;

e79.. x87*x88 - (x82*x37 + x83*x41 + x84*x45 + x85*x49 + x86*x53) =E= 0;

e80.. x87*x89 - (x82*x38 + x83*x42 + x84*x46 + x85*x50 + x86*x54) =E= 0;

e81.. x87*x90 - (x82*x39 + x83*x43 + x84*x47 + x85*x51 + x86*x55) =E= 0;

e82.. x87*x91 - (x82*x40 + x83*x44 + x84*x48 + x85*x52 + x86*x56) =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 = 10;
x13.up = 10;
x14.up = 10;
x15.up = 10;
x16.up = 10;
x17.up = 10;
x18.up = 10;
x19.up = 10;
x20.up = 10;
x21.up = 10;
x22.up = 10;
x23.up = 10;
x24.up = 10;
x25.up = 10;
x26.up = 10;
x27.up = 10;
x28.up = 10;
x29.up = 10;
x30.up = 10;
x31.up = 10;
x32.up = 1000;
x33.up = 1000;
x34.up = 1000;
x35.up = 1000;
x36.up = 1000;
x37.up = 10;
x38.up = 10;
x39.up = 10;
x40.up = 10;
x41.up = 10;
x42.up = 10;
x43.up = 10;
x44.up = 10;
x45.up = 10;
x46.up = 10;
x47.up = 10;
x48.up = 10;
x49.up = 10;
x50.up = 10;
x51.up = 10;
x52.up = 10;
x53.up = 10;
x54.up = 10;
x55.up = 10;
x56.up = 10;
x57.up = 1000;
x58.up = 1000;
x59.up = 1000;
x60.up = 1000;
x61.up = 1000;
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 = 10;
x89.up = 10;
x90.up = 10;
x91.up = 10;
x92.up = 10000;
x93.up = 10000;
x94.up = 10000;
x95.up = 10000;
x96.up = 10000;
x97.lo = 300; x97.up = 810;
x98.lo = 300; x98.up = 810;
x99.lo = 300; x99.up = 810;
x100.lo = 300; x100.up = 810;
x101.lo = 300; x101.up = 810;
x102.up = 10000;
x103.up = 10000;
x104.up = 10000;
x105.up = 10000;
x106.up = 10000;
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;
x117.up = 10000;
x118.up = 10000;
x119.up = 10000;
x120.up = 10000;
x121.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 = 0.2;
x13.l = 0.2;
x14.l = 0.2;
x15.l = 0.2;
x16.l = 0.2;
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 = 100;
x33.l = 100;
x34.l = 100;
x35.l = 100;
x36.l = 100;
x37.l = 0.2;
x38.l = 0.2;
x39.l = 0.2;
x40.l = 0.2;
x41.l = 0.2;
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 = 50;
x58.l = 50;
x59.l = 50;
x60.l = 50;
x61.l = 50;
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 = 100;
x88.l = 0.2;
x89.l = 0.2;
x90.l = 0.2;
x91.l = 0.2;
x92.l = 1;
x93.l = 1;
x94.l = 1;
x95.l = 1;
x96.l = 1;
x97.l = 400;
x98.l = 400;
x99.l = 400;
x100.l = 400;
x101.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: 2024-03-04 Git hash: 72419ac9
Imprint / Privacy Policy / License: CC-BY 4.0