MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Removed Instance ex8_3_10

Formatsⓘ ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ  
Other points (infeas > 1e-08)ⓘ  
Dual Boundsⓘ
-909090.9091 (LINDO)
-99999999809999994880. (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: 2026-09-14 Git hash: 9472b011
Imprint / Privacy Policy / License: CC-BY 4.0