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Removed Instance ex8_3_10

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)  
Other points (infeas > 1e-08)  
Dual Bounds
-909090.90910000 (LINDO)
-99999999809999994880.00000000 (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.
Source Test Problem ex8.3.10 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Removed from library 15 Aug 2014
Removed because Objective function is singular (division by variable that can be 0)
Problem type NLP
#Variables 141
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 136
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature indefinite
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 2
#Constraints 108
#Linear Constraints 43
#Quadratic Constraints 65
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 726
#Nonlinear Nonzeros in Jacobian 565
#Nonzeros in (Upper-Left) Hessian of Lagrangian 493
#Nonzeros in Diagonal of Hessian of Lagrangian 11
#Blocks in Hessian of Lagrangian 16
Minimal blocksize in Hessian of Lagrangian 6
Maximal blocksize in Hessian of Lagrangian 12
Average blocksize in Hessian of Lagrangian 8.5
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 9.5980e-03
Maximal coefficient 2.0000e+00
Infeasibility of initial point 250

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*        109      108        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        142      142        0        0        0        0        0        0
*  FX      0        0        0        0        0        0        0        0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        729      162      567        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,x122,x123,x124,x125,x126,x127,x128
          ,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141
          ,x142;

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
          ,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114
          ,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127
          ,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140
          ,x141,x142;

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,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109;


e1.. -x100/x101 - objvar =E= 0;

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

e3..  - x2 + x7 - x67 - x72 - x77 - x82 - x87 =E= 0;

e4..  - x3 + x8 - x68 - x73 - x78 - x83 - x88 =E= 0;

e5..  - x4 + x9 - x69 - x74 - x79 - x84 - x89 =E= 0;

e6..  - x5 + x10 - x70 - x75 - x80 - x85 - x90 =E= 0;

e7..  - x6 + x11 - x71 - x76 - x81 - x86 - x91 =E= 0;

e8.. x12*x7 - (x42*x67 + x47*x72 + x52*x77 + x57*x82 + x62*x87) - x2 =E= 0;

e9.. x13*x7 - (x43*x67 + x48*x72 + x53*x77 + x58*x82 + x63*x87) =E= 0;

e10.. x14*x7 - (x44*x67 + x49*x72 + x54*x77 + x59*x82 + x64*x87) =E= 0;

e11.. x15*x7 - (x45*x67 + x50*x72 + x55*x77 + x60*x82 + x65*x87) =E= 0;

e12.. x16*x7 - (x46*x67 + x51*x72 + x56*x77 + x61*x82 + x66*x87) =E= 0;

e13.. x17*x8 - (x42*x68 + x47*x73 + x52*x78 + x57*x83 + x62*x88) - x3 =E= 0;

e14.. x18*x8 - (x43*x68 + x48*x73 + x53*x78 + x58*x83 + x63*x88) =E= 0;

e15.. x19*x8 - (x44*x68 + x49*x73 + x54*x78 + x59*x83 + x64*x88) =E= 0;

e16.. x20*x8 - (x45*x68 + x50*x73 + x55*x78 + x60*x83 + x65*x88) =E= 0;

e17.. x21*x8 - (x46*x68 + x51*x73 + x56*x78 + x61*x83 + x66*x88) =E= 0;

e18.. x22*x9 - (x42*x69 + x47*x74 + x52*x79 + x57*x84 + x62*x89) - x4 =E= 0;

e19.. x23*x9 - (x43*x69 + x48*x74 + x53*x79 + x58*x84 + x63*x89) =E= 0;

e20.. x24*x9 - (x44*x69 + x49*x74 + x54*x79 + x59*x84 + x64*x89) =E= 0;

e21.. x25*x9 - (x45*x69 + x50*x74 + x55*x79 + x60*x84 + x65*x89) =E= 0;

e22.. x26*x9 - (x46*x69 + x51*x74 + x56*x79 + x61*x84 + x66*x89) =E= 0;

e23.. x27*x10 - (x42*x70 + x47*x75 + x52*x80 + x57*x85 + x62*x90) - x5 =E= 0;

e24.. x28*x10 - (x43*x70 + x48*x75 + x53*x80 + x58*x85 + x63*x90) =E= 0;

e25.. x29*x10 - (x44*x70 + x49*x75 + x54*x80 + x59*x85 + x64*x90) =E= 0;

e26.. x30*x10 - (x45*x70 + x50*x75 + x55*x80 + x60*x85 + x65*x90) =E= 0;

e27.. x31*x10 - (x46*x70 + x51*x75 + x56*x80 + x61*x85 + x66*x90) =E= 0;

e28.. x32*x11 - (x42*x71 + x47*x76 + x52*x81 + x57*x86 + x62*x91) - x6 =E= 0;

e29.. x33*x11 - (x43*x71 + x48*x76 + x53*x81 + x58*x86 + x63*x91) =E= 0;

e30.. x34*x11 - (x44*x71 + x49*x76 + x54*x81 + x59*x86 + x64*x91) =E= 0;

e31.. x35*x11 - (x45*x71 + x50*x76 + x55*x81 + x60*x86 + x65*x91) =E= 0;

e32.. x36*x11 - (x46*x71 + x51*x76 + x56*x81 + x61*x86 + x66*x91) =E= 0;

e33..  - x7 + x37 =E= 0;

e34..  - x8 + x38 =E= 0;

e35..  - x9 + x39 =E= 0;

e36..  - x10 + x40 =E= 0;

e37..  - x11 + x41 =E= 0;

e38.. x42*x37 - (x12*x7 + x103*(-x108 - x109 - 2*x112)) =E= 0;

e39.. x43*x37 - (x13*x7 + x103*(x110 - x113)) =E= 0;

e40.. x44*x37 - (x14*x7 + x103*(x111 + x112 - x114)) =E= 0;

e41.. x45*x37 - (x15*x7 + x103*(x109 - x110 - 2*x111 + x113 + 2*x114)) =E= 0;

e42.. x46*x37 - (x16*x7 + x103*x108) =E= 0;

e43.. x47*x38 - (x17*x8 + x104*(-x115 - x116 - 2*x119)) =E= 0;

e44.. x48*x38 - (x18*x8 + x104*(x117 - x120)) =E= 0;

e45.. x49*x38 - (x19*x8 + x104*(x118 + x119 - x121)) =E= 0;

e46.. x50*x38 - (x20*x8 + x104*(x116 - x117 - 2*x118 + x120 + 2*x121)) =E= 0;

e47.. x51*x38 - (x21*x8 + x104*x115) =E= 0;

e48.. x52*x39 - (x22*x9 + x105*(-x122 - x123 - 2*x126)) =E= 0;

e49.. x53*x39 - (x23*x9 + x105*(x124 - x127)) =E= 0;

e50.. x54*x39 - (x24*x9 + x105*(x125 + x126 - x128)) =E= 0;

e51.. x55*x39 - (x25*x9 + x105*(x123 - x124 - 2*x125 + x127 + 2*x128)) =E= 0;

e52.. x56*x39 - (x26*x9 + x105*x122) =E= 0;

e53.. x57*x40 - (x27*x10 + x106*(-x129 - x130 - 2*x133)) =E= 0;

e54.. x58*x40 - (x28*x10 + x106*(x131 - x134)) =E= 0;

e55.. x59*x40 - (x29*x10 + x106*(x132 + x133 - x135)) =E= 0;

e56.. x60*x40 - (x30*x10 + x106*(x130 - x131 - 2*x132 + x134 + 2*x135)) =E= 0;

e57.. x61*x40 - (x31*x10 + x106*x129) =E= 0;

e58.. x62*x41 - (x32*x11 + x107*(-x136 - x137 - 2*x140)) =E= 0;

e59.. x63*x41 - (x33*x11 + x107*(x138 - x141)) =E= 0;

e60.. x64*x41 - (x34*x11 + x107*(x139 + x140 - x142)) =E= 0;

e61.. x65*x41 - (x35*x11 + x107*(x137 - x138 - 2*x139 + x141 + 2*x142)) =E= 0;

e62.. x66*x41 - (x36*x11 + x107*x136) =E= 0;

e63..  - 0.33384*x42 + x108 =E= 0;

e64..  - 0.33384*x47 + x115 =E= 0;

e65..  - 0.33384*x52 + x122 =E= 0;

e66..  - 0.33384*x57 + x129 =E= 0;

e67..  - 0.33384*x62 + x136 =E= 0;

e68..  - 0.26687*x42 + x109 =E= 0;

e69..  - 0.26687*x47 + x116 =E= 0;

e70..  - 0.26687*x52 + x123 =E= 0;

e71..  - 0.26687*x57 + x130 =E= 0;

e72..  - 0.26687*x62 + x137 =E= 0;

e73..  - 0.1494*x45 + x110 =E= 0;

e74..  - 0.1494*x50 + x117 =E= 0;

e75..  - 0.1494*x55 + x124 =E= 0;

e76..  - 0.1494*x60 + x131 =E= 0;

e77..  - 0.1494*x65 + x138 =E= 0;

e78.. -0.18957*x45*x45 + x111 =E= 0;

e79.. -0.18957*x50*x50 + x118 =E= 0;

e80.. -0.18957*x55*x55 + x125 =E= 0;

e81.. -0.18957*x60*x60 + x132 =E= 0;

e82.. -0.18957*x65*x65 + x139 =E= 0;

e83.. -0.009598*x42*x42 + x112 =E= 0;

e84.. -0.009598*x47*x47 + x119 =E= 0;

e85.. -0.009598*x52*x52 + x126 =E= 0;

e86.. -0.009598*x57*x57 + x133 =E= 0;

e87.. -0.009598*x62*x62 + x140 =E= 0;

e88..  - 0.29425*x43 + x113 =E= 0;

e89..  - 0.29425*x48 + x120 =E= 0;

e90..  - 0.29425*x53 + x127 =E= 0;

e91..  - 0.29425*x58 + x134 =E= 0;

e92..  - 0.29425*x63 + x141 =E= 0;

e93..  - 0.011932*x44 + x114 =E= 0;

e94..  - 0.011932*x49 + x121 =E= 0;

e95..  - 0.011932*x54 + x128 =E= 0;

e96..  - 0.011932*x59 + x135 =E= 0;

e97..  - 0.011932*x64 + x142 =E= 0;

e98..    x37 - x67 - x68 - x69 - x70 - x71 - x92 =E= 0;

e99..    x38 - x72 - x73 - x74 - x75 - x76 - x93 =E= 0;

e100..    x39 - x77 - x78 - x79 - x80 - x81 - x94 =E= 0;

e101..    x40 - x82 - x83 - x84 - x85 - x86 - x95 =E= 0;

e102..    x41 - x87 - x88 - x89 - x90 - x91 - x96 =E= 0;

e103..  - x92 - x93 - x94 - x95 - x96 + x97 =E= 0;

e104.. x97*x98 - (x92*x42 + x93*x47 + x94*x52 + x95*x57 + x96*x62) =E= 0;

e105.. x97*x99 - (x92*x43 + x93*x48 + x94*x53 + x95*x58 + x96*x63) =E= 0;

e106.. x97*x100 - (x92*x44 + x93*x49 + x94*x54 + x95*x59 + x96*x64) =E= 0;

e107.. x97*x101 - (x92*x45 + x93*x50 + x94*x55 + x95*x60 + x96*x65) =E= 0;

e108.. x97*x102 - (x92*x46 + x93*x51 + x94*x56 + x95*x61 + x96*x66) =E= 0;

e109..    x103 + x104 + x105 + x106 + x107 =L= 6000;

* 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 = 10;
x33.up = 10;
x34.up = 10;
x35.up = 10;
x36.up = 10;
x37.up = 1000;
x38.up = 1000;
x39.up = 1000;
x40.up = 1000;
x41.up = 1000;
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 = 10;
x58.up = 10;
x59.up = 10;
x60.up = 10;
x61.up = 10;
x62.up = 10;
x63.up = 10;
x64.up = 10;
x65.up = 10;
x66.up = 10;
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 = 1000;
x94.up = 1000;
x95.up = 1000;
x96.up = 1000;
x97.up = 1000;
x98.up = 10;
x99.up = 10;
x100.up = 10;
x101.up = 10;
x102.up = 10;
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;
x122.up = 10000;
x123.up = 10000;
x124.up = 10000;
x125.up = 10000;
x126.up = 10000;
x127.up = 10000;
x128.up = 10000;
x129.up = 10000;
x130.up = 10000;
x131.up = 10000;
x132.up = 10000;
x133.up = 10000;
x134.up = 10000;
x135.up = 10000;
x136.up = 10000;
x137.up = 10000;
x138.up = 10000;
x139.up = 10000;
x140.up = 10000;
x141.up = 10000;
x142.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 = 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 = 0.2;
x63.l = 0.2;
x64.l = 0.2;
x65.l = 0.2;
x66.l = 0.2;
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 = 50;
x93.l = 50;
x94.l = 50;
x95.l = 50;
x96.l = 50;
x97.l = 100;
x98.l = 0.2;
x99.l = 0.2;
x100.l = 0.2;
x101.l = 0.2;
x102.l = 0.2;
x103.l = 1;
x104.l = 1;
x105.l = 1;
x106.l = 1;
x107.l = 1;

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: 2022-05-24 Git hash: 1198c186
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