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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: powerflow0014r

Optimal Power Flow problem modeled using quadratic functions (rectangular coordinates)
Formats ams gms lp mod nl osil pip
Primal Bounds (infeas ≤ 1e-08)
8082.58169000 p1 ( gdx sol )
(infeas: 4e-13)
Other points (infeas > 1e-08)  
Dual Bounds
0.00000000 (ANTIGONE)
0.00000000 (BARON)
0.00000000 (COUENNE)
0.00000000 (LINDO)
0.00000000 (SCIP)
References Hijazi, H L, Coffrin, C, and Van Hentenryck, P, Convex Quadratic Relaxations of Nonlinear Programs in Power Systems, Tech. Rep. 2013-09, Optimization Online, 2013.
Application Electricity Networks
Added to library 18 Aug 2014
Problem type QCQP
#Variables 118
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 113
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 5
#Nonlinear Nonzeros in Objective 5
#Constraints 197
#Linear Constraints 49
#Quadratic Constraints 148
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 647
#Nonlinear Nonzeros in Jacobian 456
#Nonzeros in (Upper-Left) Hessian of Lagrangian 273
#Nonzeros in Diagonal of Hessian of Lagrangian 113
#Blocks in Hessian of Lagrangian 86
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 28
Average blocksize in Hessian of Lagrangian 1.313953
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0.942
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
*        198      110       24       64        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        119      119        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        653      192      461        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,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,objvar;

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,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
          ,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
          ,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
          ,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
          ,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
          ,e195,e196,e197,e198;


e1.. 430.293*sqr(x109) + 2000*x109 + 2500*sqr(x110) + 2000*x110 + 100*sqr(x111)
      + 4000*x111 + 100*sqr(x112) + 4000*x112 + 100*sqr(x113) + 4000*x113
      - objvar =E= 0;

e2.. 0.567509596153698*x82*x83 - 1.1350191923074*sqr(x82) - 2.39093157587886*
     x82*x97 + 0.567509596153698*x83*x82 + 2.39093157587886*x83*x96 + 
     2.39093157587886*x96*x83 - 1.1350191923074*sqr(x96) + 0.567509596153698*
     x96*x97 - 2.39093157587886*x97*x82 + 0.567509596153698*x97*x96 + x1 =E= 0;

e3.. 0.567509596153698*x82*x83 + 2.39093157587886*x82*x97 + 0.567509596153698*
     x83*x82 - 1.1350191923074*sqr(x83) - 2.39093157587886*x83*x96 - 
     2.39093157587886*x96*x83 + 0.567509596153698*x96*x97 + 2.39093157587886*
     x97*x82 + 0.567509596153698*x97*x96 - 1.1350191923074*sqr(x97) + x2 =E= 0;

e4.. 4.54504135987637*x89*x101 - 4.54504135987637*x87*x103 + 4.54504135987637*
     x101*x89 - 4.54504135987637*x103*x87 + x3 =E= 0;

e5.. 4.54504135987637*x87*x103 - 4.54504135987637*x89*x101 - 4.54504135987637*
     x101*x89 + 4.54504135987637*x103*x87 + x4 =E= 0;

e6.. 0.9404423768502*x90*x91 - 1.8808847537004*sqr(x90) - 2.20147187473026*x90*
     x105 + 0.9404423768502*x91*x90 + 2.20147187473026*x91*x104 + 
     2.20147187473026*x104*x91 - 1.8808847537004*sqr(x104) + 0.9404423768502*
     x104*x105 - 2.20147187473026*x105*x90 + 0.9404423768502*x105*x104 + x5
      =E= 0;

e7.. 0.9404423768502*x90*x91 + 2.20147187473026*x90*x105 + 0.9404423768502*x91*
     x90 - 1.8808847537004*sqr(x91) - 2.20147187473026*x91*x104 - 
     2.20147187473026*x104*x91 + 0.9404423768502*x104*x105 + 2.20147187473026*
     x105*x90 + 0.9404423768502*x105*x104 - 1.8808847537004*sqr(x105) + x6
      =E= 0;

e8.. 2.39097169089518*x87*x98 - 2.39097169089518*x84*x101 + 2.39097169089518*
     x98*x87 - 2.39097169089518*x101*x84 + x7 =E= 0;

e9.. 2.39097169089518*x84*x101 - 2.39097169089518*x87*x98 - 2.39097169089518*
     x98*x87 + 2.39097169089518*x101*x84 + x8 =E= 0;

e10.. 1.98396952622808*x86*x99 - 1.98396952622808*x85*x100 + 1.98396952622808*
      x99*x86 - 1.98396952622808*x100*x85 + x9 =E= 0;

e11.. 1.98396952622808*x85*x100 - 1.98396952622808*x86*x99 - 1.98396952622808*
      x99*x86 + 1.98396952622808*x100*x85 + x10 =E= 0;

e12.. 0.712002743509966*x89*x94 - 1.42400548701993*sqr(x89) - 1.5145252284653*
      x89*x108 + 0.712002743509966*x94*x89 + 1.5145252284653*x94*x103 + 
      1.5145252284653*x103*x94 - 1.42400548701993*sqr(x103) + 0.712002743509966
      *x103*x108 - 1.5145252284653*x108*x89 + 0.712002743509966*x108*x103 + x11
       =E= 0;

e13.. 0.712002743509966*x89*x94 + 1.5145252284653*x89*x108 + 0.712002743509966*
      x94*x89 - 1.42400548701993*sqr(x94) - 1.5145252284653*x94*x103 - 
      1.5145252284653*x103*x94 + 0.712002743509966*x103*x108 + 1.5145252284653*
      x108*x89 + 0.712002743509966*x108*x103 - 1.42400548701993*sqr(x108) + x12
       =E= 0;

e14.. 3.42049033074784*x84*x85 - 6.84098066149567*sqr(x84) - 10.7892769908458*
      x84*x99 + 3.42049033074784*x85*x84 + 10.7892769908458*x85*x98 + 
      10.7892769908458*x98*x85 - 6.84098066149567*sqr(x98) + 3.42049033074784*
      x98*x99 - 10.7892769908458*x99*x84 + 3.42049033074784*x99*x98 + x13 =E= 0
      ;

e15.. 3.42049033074784*x84*x85 + 10.7892769908458*x84*x99 + 3.42049033074784*
      x85*x84 - 6.84098066149567*sqr(x85) - 10.7892769908458*x85*x98 - 
      10.7892769908458*x98*x85 + 3.42049033074784*x98*x99 + 10.7892769908458*
      x99*x84 + 3.42049033074784*x99*x98 - 6.84098066149567*sqr(x99) + x14
       =E= 0;

e16.. 1.54946370191899*x86*x93 - 3.09892740383799*sqr(x86) - 3.05137772409656*
      x86*x107 + 1.54946370191899*x93*x86 + 3.05137772409656*x93*x100 + 
      3.05137772409656*x100*x93 - 3.09892740383799*sqr(x100) + 1.54946370191899
      *x100*x107 - 3.05137772409656*x107*x86 + 1.54946370191899*x107*x100 + x15
       =E= 0;

e17.. 1.54946370191899*x86*x93 + 3.05137772409656*x86*x107 + 1.54946370191899*
      x93*x86 - 3.09892740383799*sqr(x93) - 3.05137772409656*x93*x100 - 
      3.05137772409656*x100*x93 + 1.54946370191899*x100*x107 + 3.05137772409656
      *x107*x86 + 1.54946370191899*x107*x100 - 3.09892740383799*sqr(x107) + x16
       =E= 0;

e18.. 2.83848992336077*x88*x101 - 2.83848992336077*x87*x102 + 2.83848992336077*
      x101*x88 - 2.83848992336077*x102*x87 + x17 =E= 0;

e19.. 2.83848992336077*x87*x102 - 2.83848992336077*x88*x101 - 2.83848992336077*
      x101*x88 + 2.83848992336077*x102*x87 + x18 =E= 0;

e20.. 0.568497078903163*x93*x94 - 1.13699415780633*sqr(x93) - 1.15748173755268*
      x93*x108 + 0.568497078903163*x94*x93 + 1.15748173755268*x94*x107 + 
      1.15748173755268*x107*x94 - 1.13699415780633*sqr(x107) + 
      0.568497078903163*x107*x108 - 1.15748173755268*x108*x93 + 
      0.568497078903163*x108*x107 + x19 =E= 0;

e21.. 0.568497078903163*x93*x94 + 1.15748173755268*x93*x108 + 0.568497078903163
      *x94*x93 - 1.13699415780633*sqr(x94) - 1.15748173755268*x94*x107 - 
      1.15748173755268*x107*x94 + 0.568497078903163*x107*x108 + 
      1.15748173755268*x108*x93 + 0.568497078903163*x108*x107 - 
      1.13699415780633*sqr(x108) + x20 =E= 0;

e22.. 0.762983720225487*x86*x92 - 1.52596744045097*sqr(x86) - 1.5879819825147*
      x86*x106 + 0.762983720225487*x92*x86 + 1.5879819825147*x92*x100 + 
      1.5879819825147*x100*x92 - 1.52596744045097*sqr(x100) + 0.762983720225487
      *x100*x106 - 1.5879819825147*x106*x86 + 0.762983720225487*x106*x100 + x21
       =E= 0;

e23.. 0.762983720225487*x86*x92 + 1.5879819825147*x86*x106 + 0.762983720225487*
      x92*x86 - 1.52596744045097*sqr(x92) - 1.5879819825147*x92*x100 - 
      1.5879819825147*x100*x92 + 0.762983720225487*x100*x106 + 1.5879819825147*
      x106*x86 + 0.762983720225487*x106*x100 - 1.52596744045097*sqr(x106) + x22
       =E= 0;

e24.. 0.97751428158863*x86*x91 - 1.95502856317726*sqr(x86) - 2.04703717212022*
      x86*x105 + 0.97751428158863*x91*x86 + 2.04703717212022*x91*x100 + 
      2.04703717212022*x100*x91 - 1.95502856317726*sqr(x100) + 0.97751428158863
      *x100*x105 - 2.04703717212022*x105*x86 + 0.97751428158863*x105*x100 + x23
       =E= 0;

e25.. 0.97751428158863*x86*x91 + 2.04703717212022*x86*x105 + 0.97751428158863*
      x91*x86 - 1.95502856317726*sqr(x91) - 2.04703717212022*x91*x100 - 
      2.04703717212022*x100*x91 + 0.97751428158863*x100*x105 + 2.04703717212022
      *x105*x86 + 0.97751428158863*x105*x100 - 1.95502856317726*sqr(x105) + x24
       =E= 0;

e26.. 1.24451229341096*x92*x93 - 2.48902458682192*sqr(x92) - 1.12598731308611*
      x92*x107 + 1.24451229341096*x93*x92 + 1.12598731308611*x93*x106 + 
      1.12598731308611*x106*x93 - 2.48902458682192*sqr(x106) + 1.24451229341096
      *x106*x107 - 1.12598731308611*x107*x92 + 1.24451229341096*x107*x106 + x25
       =E= 0;

e27.. 1.24451229341096*x92*x93 + 1.12598731308611*x92*x107 + 1.24451229341096*
      x93*x92 - 2.48902458682192*sqr(x93) - 1.12598731308611*x93*x106 - 
      1.12598731308611*x106*x93 + 1.24451229341096*x106*x107 + 1.12598731308611
      *x107*x92 + 1.24451229341096*x107*x106 - 2.48902458682192*sqr(x107) + x26
       =E= 0;

e28.. 0.512948727485094*x81*x85 - 1.02589745497019*sqr(x81) - 2.11749184116742*
      x81*x99 + 0.512948727485094*x85*x81 + 2.11749184116742*x85*x95 + 
      2.11749184116742*x95*x85 - 1.02589745497019*sqr(x95) + 0.512948727485094*
      x95*x99 - 2.11749184116742*x99*x81 + 0.512948727485094*x99*x95 + x27
       =E= 0;

e29.. 0.512948727485094*x81*x85 + 2.11749184116742*x81*x99 + 0.512948727485094*
      x85*x81 - 1.02589745497019*sqr(x85) - 2.11749184116742*x85*x95 - 
      2.11749184116742*x95*x85 + 0.512948727485094*x95*x99 + 2.11749184116742*
      x99*x81 + 0.512948727485094*x99*x95 - 1.02589745497019*sqr(x99) + x28
       =E= 0;

e30.. 1.95102477622371*x89*x90 - 3.90204955244743*sqr(x89) - 5.18269706353046*
      x89*x104 + 1.95102477622371*x90*x89 + 5.18269706353046*x90*x103 + 
      5.18269706353046*x103*x90 - 3.90204955244743*sqr(x103) + 1.95102477622371
      *x103*x104 - 5.18269706353046*x104*x89 + 1.95102477622371*x104*x103 + x29
       =E= 0;

e31.. 1.95102477622371*x89*x90 + 5.18269706353046*x89*x104 + 1.95102477622371*
      x90*x89 - 3.90204955244743*sqr(x90) - 5.18269706353046*x90*x103 - 
      5.18269706353046*x103*x90 + 1.95102477622371*x103*x104 + 5.18269706353046
      *x104*x89 + 1.95102477622371*x104*x103 - 3.90204955244743*sqr(x104) + x30
       =E= 0;

e32.. 2.49956580039902*x81*x82 - 4.99913160079803*sqr(x81) - 7.63154326158978*
      x81*x96 + 2.49956580039902*x82*x81 + 7.63154326158978*x82*x95 + 
      7.63154326158978*x95*x82 - 4.99913160079803*sqr(x95) + 2.49956580039902*
      x95*x96 - 7.63154326158978*x96*x81 + 2.49956580039902*x96*x95 + x31 =E= 0
      ;

e33.. 2.49956580039902*x81*x82 + 7.63154326158978*x81*x96 + 2.49956580039902*
      x82*x81 - 4.99913160079803*sqr(x82) - 7.63154326158978*x82*x95 - 
      7.63154326158978*x95*x82 + 2.49956580039902*x95*x96 + 7.63154326158978*
      x96*x81 + 2.49956580039902*x96*x95 - 4.99913160079803*sqr(x96) + x32
       =E= 0;

e34.. 0.850569833547202*x82*x85 - 1.7011396670944*sqr(x82) - 2.59696369898486*
      x82*x99 + 0.850569833547202*x85*x82 + 2.59696369898486*x85*x96 + 
      2.59696369898486*x96*x85 - 1.7011396670944*sqr(x96) + 0.850569833547202*
      x96*x99 - 2.59696369898486*x99*x82 + 0.850569833547202*x99*x96 + x33
       =E= 0;

e35.. 0.850569833547202*x82*x85 + 2.59696369898486*x82*x99 + 0.850569833547202*
      x85*x82 - 1.7011396670944*sqr(x85) - 2.59696369898486*x85*x96 - 
      2.59696369898486*x96*x85 + 0.850569833547202*x96*x99 + 2.59696369898486*
      x99*x82 + 0.850569833547202*x99*x96 - 1.7011396670944*sqr(x99) + x34
       =E= 0;

e36.. 0.99298785496278*x83*x84 - 1.98597570992556*sqr(x83) - 2.53440848879696*
      x83*x98 + 0.99298785496278*x84*x83 + 2.53440848879696*x84*x97 + 
      2.53440848879696*x97*x84 - 1.98597570992556*sqr(x97) + 0.99298785496278*
      x97*x98 - 2.53440848879696*x98*x83 + 0.99298785496278*x98*x97 + x35 =E= 0
      ;

e37.. 0.99298785496278*x83*x84 + 2.53440848879696*x83*x98 + 0.99298785496278*
      x84*x83 - 1.98597570992556*sqr(x84) - 2.53440848879696*x84*x97 - 
      2.53440848879696*x97*x84 + 0.99298785496278*x97*x98 + 2.53440848879696*
      x98*x83 + 0.99298785496278*x98*x97 - 1.98597570992556*sqr(x98) + x36
       =E= 0;

e38.. 0.898989535761804*x89*x98 - 0.898989535761804*x84*x103 + 
      0.898989535761804*x98*x89 - 0.898989535761804*x103*x84 + x37 =E= 0;

e39.. 0.898989535761804*x84*x103 - 0.898989535761804*x89*x98 - 
      0.898989535761804*x98*x89 + 0.898989535761804*x103*x84 + x38 =E= 0;

e40.. 0.843016575307471*x82*x84 - 1.68603315061494*sqr(x82) - 2.55791916293604*
      x82*x98 + 0.843016575307471*x84*x82 + 2.55791916293604*x84*x96 + 
      2.55791916293604*x96*x84 - 1.68603315061494*sqr(x96) + 0.843016575307471*
      x96*x98 - 2.55791916293604*x98*x82 + 0.843016575307471*x98*x96 + x39
       =E= 0;

e41.. 0.843016575307471*x82*x84 + 2.55791916293604*x82*x98 + 0.843016575307471*
      x84*x82 - 1.68603315061494*sqr(x84) - 2.55791916293604*x84*x96 - 
      2.55791916293604*x96*x84 + 0.843016575307471*x96*x98 + 2.55791916293604*
      x98*x82 + 0.843016575307471*x98*x96 - 1.68603315061494*sqr(x98) + x40
       =E= 0;

e42.. 2.39093157587886*x82*x83 - 4.75996315175772*sqr(x82) + 0.567509596153698*
      x82*x97 + 2.39093157587886*x83*x82 - 0.567509596153698*x83*x96 - 
      0.567509596153698*x96*x83 - 4.75996315175772*sqr(x96) + 2.39093157587886*
      x96*x97 + 0.567509596153698*x97*x82 + 2.39093157587886*x97*x96 + x41
       =E= 0;

e43.. 2.39093157587886*x82*x83 - 0.567509596153698*x82*x97 + 2.39093157587886*
      x83*x82 - 4.75996315175772*sqr(x83) + 0.567509596153698*x83*x96 + 
      0.567509596153698*x96*x83 + 2.39093157587886*x96*x97 - 0.567509596153698*
      x97*x82 + 2.39093157587886*x97*x96 - 4.75996315175772*sqr(x97) + x42
       =E= 0;

e44.. 4.54504135987637*x87*x89 - 9.09008271975275*sqr(x87) + 4.54504135987637*
      x89*x87 - 9.09008271975275*sqr(x101) + 4.54504135987637*x101*x103 + 
      4.54504135987637*x103*x101 + x43 =E= 0;

e45.. 4.54504135987637*x87*x89 + 4.54504135987637*x89*x87 - 9.09008271975275*
      sqr(x89) + 4.54504135987637*x101*x103 + 4.54504135987637*x103*x101 - 
      9.09008271975275*sqr(x103) + x44 =E= 0;

e46.. 2.20147187473026*x90*x91 - 4.40294374946052*sqr(x90) + 0.9404423768502*
      x90*x105 + 2.20147187473026*x91*x90 - 0.9404423768502*x91*x104 - 
      0.9404423768502*x104*x91 - 4.40294374946052*sqr(x104) + 2.20147187473026*
      x104*x105 + 0.9404423768502*x105*x90 + 2.20147187473026*x105*x104 + x45
       =E= 0;

e47.. 2.20147187473026*x90*x91 - 0.9404423768502*x90*x105 + 2.20147187473026*
      x91*x90 - 4.40294374946052*sqr(x91) + 0.9404423768502*x91*x104 + 
      0.9404423768502*x104*x91 + 2.20147187473026*x104*x105 - 0.9404423768502*
      x105*x90 + 2.20147187473026*x105*x104 - 4.40294374946052*sqr(x105) + x46
       =E= 0;

e48.. 2.39097169089518*x84*x87 - 4.78194338179036*sqr(x84) + 2.39097169089518*
      x87*x84 - 4.78194338179036*sqr(x98) + 2.39097169089518*x98*x101 + 
      2.39097169089518*x101*x98 + x47 =E= 0;

e49.. 2.39097169089518*x84*x87 + 2.39097169089518*x87*x84 - 4.78194338179036*
      sqr(x87) + 2.39097169089518*x98*x101 + 2.39097169089518*x101*x98 - 
      4.78194338179036*sqr(x101) + x48 =E= 0;

e50.. 1.98396952622808*x85*x86 - 3.96793905245615*sqr(x85) + 1.98396952622808*
      x86*x85 - 3.96793905245615*sqr(x99) + 1.98396952622808*x99*x100 + 
      1.98396952622808*x100*x99 + x49 =E= 0;

e51.. 1.98396952622808*x85*x86 + 1.98396952622808*x86*x85 - 3.96793905245615*
      sqr(x86) + 1.98396952622808*x99*x100 + 1.98396952622808*x100*x99 - 
      3.96793905245615*sqr(x100) + x50 =E= 0;

e52.. 1.5145252284653*x89*x94 - 3.0290504569306*sqr(x89) + 0.712002743509966*
      x89*x108 + 1.5145252284653*x94*x89 - 0.712002743509966*x94*x103 - 
      0.712002743509966*x103*x94 - 3.0290504569306*sqr(x103) + 1.5145252284653*
      x103*x108 + 0.712002743509966*x108*x89 + 1.5145252284653*x108*x103 + x51
       =E= 0;

e53.. 1.5145252284653*x89*x94 - 0.712002743509966*x89*x108 + 1.5145252284653*
      x94*x89 - 3.0290504569306*sqr(x94) + 0.712002743509966*x94*x103 + 
      0.712002743509966*x103*x94 + 1.5145252284653*x103*x108 - 
      0.712002743509966*x108*x89 + 1.5145252284653*x108*x103 - 3.0290504569306*
      sqr(x108) + x52 =E= 0;

e54.. 10.7892769908458*x84*x85 - 21.5785539816916*sqr(x84) + 3.42049033074784*
      x84*x99 + 10.7892769908458*x85*x84 - 3.42049033074784*x85*x98 - 
      3.42049033074784*x98*x85 - 21.5785539816916*sqr(x98) + 10.7892769908458*
      x98*x99 + 3.42049033074784*x99*x84 + 10.7892769908458*x99*x98 + x53 =E= 0
      ;

e55.. 10.7892769908458*x84*x85 - 3.42049033074784*x84*x99 + 10.7892769908458*
      x85*x84 - 21.5785539816916*sqr(x85) + 3.42049033074784*x85*x98 + 
      3.42049033074784*x98*x85 + 10.7892769908458*x98*x99 - 3.42049033074784*
      x99*x84 + 10.7892769908458*x99*x98 - 21.5785539816916*sqr(x99) + x54
       =E= 0;

e56.. 3.05137772409656*x86*x93 - 6.10275544819311*sqr(x86) + 1.54946370191899*
      x86*x107 + 3.05137772409656*x93*x86 - 1.54946370191899*x93*x100 - 
      1.54946370191899*x100*x93 - 6.10275544819311*sqr(x100) + 3.05137772409656
      *x100*x107 + 1.54946370191899*x107*x86 + 3.05137772409656*x107*x100 + x55
       =E= 0;

e57.. 3.05137772409656*x86*x93 - 1.54946370191899*x86*x107 + 3.05137772409656*
      x93*x86 - 6.10275544819311*sqr(x93) + 1.54946370191899*x93*x100 + 
      1.54946370191899*x100*x93 + 3.05137772409656*x100*x107 - 1.54946370191899
      *x107*x86 + 3.05137772409656*x107*x100 - 6.10275544819311*sqr(x107) + x56
       =E= 0;

e58.. 2.83848992336077*x87*x88 - 5.67697984672154*sqr(x87) + 2.83848992336077*
      x88*x87 - 5.67697984672154*sqr(x101) + 2.83848992336077*x101*x102 + 
      2.83848992336077*x102*x101 + x57 =E= 0;

e59.. 2.83848992336077*x87*x88 + 2.83848992336077*x88*x87 - 5.67697984672154*
      sqr(x88) + 2.83848992336077*x101*x102 + 2.83848992336077*x102*x101 - 
      5.67697984672154*sqr(x102) + x58 =E= 0;

e60.. 1.15748173755268*x93*x94 - 2.31496347510535*sqr(x93) + 0.568497078903163*
      x93*x108 + 1.15748173755268*x94*x93 - 0.568497078903163*x94*x107 - 
      0.568497078903163*x107*x94 - 2.31496347510535*sqr(x107) + 
      1.15748173755268*x107*x108 + 0.568497078903163*x108*x93 + 
      1.15748173755268*x108*x107 + x59 =E= 0;

e61.. 1.15748173755268*x93*x94 - 0.568497078903163*x93*x108 + 1.15748173755268*
      x94*x93 - 2.31496347510535*sqr(x94) + 0.568497078903163*x94*x107 + 
      0.568497078903163*x107*x94 + 1.15748173755268*x107*x108 - 
      0.568497078903163*x108*x93 + 1.15748173755268*x108*x107 - 
      2.31496347510535*sqr(x108) + x60 =E= 0;

e62.. 1.5879819825147*x86*x92 - 3.1759639650294*sqr(x86) + 0.762983720225487*
      x86*x106 + 1.5879819825147*x92*x86 - 0.762983720225487*x92*x100 - 
      0.762983720225487*x100*x92 - 3.1759639650294*sqr(x100) + 1.5879819825147*
      x100*x106 + 0.762983720225487*x106*x86 + 1.5879819825147*x106*x100 + x61
       =E= 0;

e63.. 1.5879819825147*x86*x92 - 0.762983720225487*x86*x106 + 1.5879819825147*
      x92*x86 - 3.1759639650294*sqr(x92) + 0.762983720225487*x92*x100 + 
      0.762983720225487*x100*x92 + 1.5879819825147*x100*x106 - 
      0.762983720225487*x106*x86 + 1.5879819825147*x106*x100 - 3.1759639650294*
      sqr(x106) + x62 =E= 0;

e64.. 2.04703717212022*x86*x91 - 4.09407434424044*sqr(x86) + 0.97751428158863*
      x86*x105 + 2.04703717212022*x91*x86 - 0.97751428158863*x91*x100 - 
      0.97751428158863*x100*x91 - 4.09407434424044*sqr(x100) + 2.04703717212022
      *x100*x105 + 0.97751428158863*x105*x86 + 2.04703717212022*x105*x100 + x63
       =E= 0;

e65.. 2.04703717212022*x86*x91 - 0.97751428158863*x86*x105 + 2.04703717212022*
      x91*x86 - 4.09407434424044*sqr(x91) + 0.97751428158863*x91*x100 + 
      0.97751428158863*x100*x91 + 2.04703717212022*x100*x105 - 0.97751428158863
      *x105*x86 + 2.04703717212022*x105*x100 - 4.09407434424044*sqr(x105) + x64
       =E= 0;

e66.. 1.12598731308611*x92*x93 - 2.25197462617221*sqr(x92) + 1.24451229341096*
      x92*x107 + 1.12598731308611*x93*x92 - 1.24451229341096*x93*x106 - 
      1.24451229341096*x106*x93 - 2.25197462617221*sqr(x106) + 1.12598731308611
      *x106*x107 + 1.24451229341096*x107*x92 + 1.12598731308611*x107*x106 + x65
       =E= 0;

e67.. 1.12598731308611*x92*x93 - 1.24451229341096*x92*x107 + 1.12598731308611*
      x93*x92 - 2.25197462617221*sqr(x93) + 1.24451229341096*x93*x106 + 
      1.24451229341096*x106*x93 + 1.12598731308611*x106*x107 - 1.24451229341096
      *x107*x92 + 1.12598731308611*x107*x106 - 2.25197462617221*sqr(x107) + x66
       =E= 0;

e68.. 2.11749184116742*x81*x85 - 4.21038368233483*sqr(x81) + 0.512948727485094*
      x81*x99 + 2.11749184116742*x85*x81 - 0.512948727485094*x85*x95 - 
      0.512948727485094*x95*x85 - 4.21038368233483*sqr(x95) + 2.11749184116742*
      x95*x99 + 0.512948727485094*x99*x81 + 2.11749184116742*x99*x95 + x67
       =E= 0;

e69.. 2.11749184116742*x81*x85 - 0.512948727485094*x81*x99 + 2.11749184116742*
      x85*x81 - 4.21038368233483*sqr(x85) + 0.512948727485094*x85*x95 + 
      0.512948727485094*x95*x85 + 2.11749184116742*x95*x99 - 0.512948727485094*
      x99*x81 + 2.11749184116742*x99*x95 - 4.21038368233483*sqr(x99) + x68
       =E= 0;

e70.. 5.18269706353046*x89*x90 - 10.3653941270609*sqr(x89) + 1.95102477622371*
      x89*x104 + 5.18269706353046*x90*x89 - 1.95102477622371*x90*x103 - 
      1.95102477622371*x103*x90 - 10.3653941270609*sqr(x103) + 5.18269706353046
      *x103*x104 + 1.95102477622371*x104*x89 + 5.18269706353046*x104*x103 + x69
       =E= 0;

e71.. 5.18269706353046*x89*x90 - 1.95102477622371*x89*x104 + 5.18269706353046*
      x90*x89 - 10.3653941270609*sqr(x90) + 1.95102477622371*x90*x103 + 
      1.95102477622371*x103*x90 + 5.18269706353046*x103*x104 - 1.95102477622371
      *x104*x89 + 5.18269706353046*x104*x103 - 10.3653941270609*sqr(x104) + x70
       =E= 0;

e72.. 7.63154326158978*x81*x82 - 15.2366865231796*sqr(x81) + 2.49956580039902*
      x81*x96 + 7.63154326158978*x82*x81 - 2.49956580039902*x82*x95 - 
      2.49956580039902*x95*x82 - 15.2366865231796*sqr(x95) + 7.63154326158978*
      x95*x96 + 2.49956580039902*x96*x81 + 7.63154326158978*x96*x95 + x71 =E= 0
      ;

e73.. 7.63154326158978*x81*x82 - 2.49956580039902*x81*x96 + 7.63154326158978*
      x82*x81 - 15.2366865231796*sqr(x82) + 2.49956580039902*x82*x95 + 
      2.49956580039902*x95*x82 + 7.63154326158978*x95*x96 - 2.49956580039902*
      x96*x81 + 7.63154326158978*x96*x95 - 15.2366865231796*sqr(x96) + x72
       =E= 0;

e74.. 2.59696369898486*x82*x85 - 5.17662739796971*sqr(x82) + 0.850569833547202*
      x82*x99 + 2.59696369898486*x85*x82 - 0.850569833547202*x85*x96 - 
      0.850569833547202*x96*x85 - 5.17662739796971*sqr(x96) + 2.59696369898486*
      x96*x99 + 0.850569833547202*x99*x82 + 2.59696369898486*x99*x96 + x73
       =E= 0;

e75.. 2.59696369898486*x82*x85 - 0.850569833547202*x82*x99 + 2.59696369898486*
      x85*x82 - 5.17662739796971*sqr(x85) + 0.850569833547202*x85*x96 + 
      0.850569833547202*x96*x85 + 2.59696369898486*x96*x99 - 0.850569833547202*
      x99*x82 + 2.59696369898486*x99*x96 - 5.17662739796971*sqr(x99) + x74
       =E= 0;

e76.. 2.53440848879696*x83*x84 - 5.06241697759392*sqr(x83) + 0.99298785496278*
      x83*x98 + 2.53440848879696*x84*x83 - 0.99298785496278*x84*x97 - 
      0.99298785496278*x97*x84 - 5.06241697759392*sqr(x97) + 2.53440848879696*
      x97*x98 + 0.99298785496278*x98*x83 + 2.53440848879696*x98*x97 + x75 =E= 0
      ;

e77.. 2.53440848879696*x83*x84 - 0.99298785496278*x83*x98 + 2.53440848879696*
      x84*x83 - 5.06241697759392*sqr(x84) + 0.99298785496278*x84*x97 + 
      0.99298785496278*x97*x84 + 2.53440848879696*x97*x98 - 0.99298785496278*
      x98*x83 + 2.53440848879696*x98*x97 - 5.06241697759392*sqr(x98) + x76
       =E= 0;

e78.. 0.898989535761804*x84*x89 - 1.79797907152361*sqr(x84) + 0.898989535761804
      *x89*x84 - 1.79797907152361*sqr(x98) + 0.898989535761804*x98*x103 + 
      0.898989535761804*x103*x98 + x77 =E= 0;

e79.. 0.898989535761804*x84*x89 + 0.898989535761804*x89*x84 - 1.79797907152361*
      sqr(x89) + 0.898989535761804*x98*x103 + 0.898989535761804*x103*x98 - 
      1.79797907152361*sqr(x103) + x78 =E= 0;

e80.. 2.55791916293604*x82*x84 - 5.09883832587208*sqr(x82) + 0.843016575307471*
      x82*x98 + 2.55791916293604*x84*x82 - 0.843016575307471*x84*x96 - 
      0.843016575307471*x96*x84 - 5.09883832587208*sqr(x96) + 2.55791916293604*
      x96*x98 + 0.843016575307471*x98*x82 + 2.55791916293604*x98*x96 + x79
       =E= 0;

e81.. 2.55791916293604*x82*x84 - 0.843016575307471*x82*x98 + 2.55791916293604*
      x84*x82 - 5.09883832587208*sqr(x84) + 0.843016575307471*x84*x96 + 
      0.843016575307471*x96*x84 + 2.55791916293604*x96*x98 - 0.843016575307471*
      x98*x82 + 2.55791916293604*x98*x96 - 5.09883832587208*sqr(x98) + x80
       =E= 0;

e82.. sqr(x1) + sqr(x41) =L= 9801;

e83.. sqr(x2) + sqr(x42) =L= 9801;

e84.. sqr(x3) + sqr(x43) =L= 9801;

e85.. sqr(x4) + sqr(x44) =L= 9801;

e86.. sqr(x5) + sqr(x45) =L= 9801;

e87.. sqr(x6) + sqr(x46) =L= 9801;

e88.. sqr(x7) + sqr(x47) =L= 9801;

e89.. sqr(x8) + sqr(x48) =L= 9801;

e90.. sqr(x9) + sqr(x49) =L= 9801;

e91.. sqr(x10) + sqr(x50) =L= 9801;

e92.. sqr(x11) + sqr(x51) =L= 9801;

e93.. sqr(x12) + sqr(x52) =L= 9801;

e94.. sqr(x13) + sqr(x53) =L= 9801;

e95.. sqr(x14) + sqr(x54) =L= 9801;

e96.. sqr(x15) + sqr(x55) =L= 9801;

e97.. sqr(x16) + sqr(x56) =L= 9801;

e98.. sqr(x17) + sqr(x57) =L= 9801;

e99.. sqr(x18) + sqr(x58) =L= 9801;

e100.. sqr(x19) + sqr(x59) =L= 9801;

e101.. sqr(x20) + sqr(x60) =L= 9801;

e102.. sqr(x21) + sqr(x61) =L= 9801;

e103.. sqr(x22) + sqr(x62) =L= 9801;

e104.. sqr(x23) + sqr(x63) =L= 9801;

e105.. sqr(x24) + sqr(x64) =L= 9801;

e106.. sqr(x25) + sqr(x65) =L= 9801;

e107.. sqr(x26) + sqr(x66) =L= 9801;

e108.. sqr(x27) + sqr(x67) =L= 9801;

e109.. sqr(x28) + sqr(x68) =L= 9801;

e110.. sqr(x29) + sqr(x69) =L= 9801;

e111.. sqr(x30) + sqr(x70) =L= 9801;

e112.. sqr(x31) + sqr(x71) =L= 9801;

e113.. sqr(x32) + sqr(x72) =L= 9801;

e114.. sqr(x33) + sqr(x73) =L= 9801;

e115.. sqr(x34) + sqr(x74) =L= 9801;

e116.. sqr(x35) + sqr(x75) =L= 9801;

e117.. sqr(x36) + sqr(x76) =L= 9801;

e118.. sqr(x37) + sqr(x77) =L= 9801;

e119.. sqr(x38) + sqr(x78) =L= 9801;

e120.. sqr(x39) + sqr(x79) =L= 9801;

e121.. sqr(x40) + sqr(x80) =L= 9801;

e122.. sqr(x81) + sqr(x95) =L= 1.1236;

e123.. sqr(x82) + sqr(x96) =L= 1.1236;

e124.. sqr(x83) + sqr(x97) =L= 1.1236;

e125.. sqr(x84) + sqr(x98) =L= 1.1236;

e126.. sqr(x85) + sqr(x99) =L= 1.1236;

e127.. sqr(x86) + sqr(x100) =L= 1.1236;

e128.. sqr(x87) + sqr(x101) =L= 1.1236;

e129.. sqr(x88) + sqr(x102) =L= 1.1236;

e130.. sqr(x89) + sqr(x103) =L= 1.1236;

e131.. sqr(x90) + sqr(x104) =L= 1.1236;

e132.. sqr(x91) + sqr(x105) =L= 1.1236;

e133.. sqr(x92) + sqr(x106) =L= 1.1236;

e134.. sqr(x93) + sqr(x107) =L= 1.1236;

e135.. sqr(x94) + sqr(x108) =L= 1.1236;

e136.. sqr(x81) + sqr(x95) =G= 0.8836;

e137.. sqr(x82) + sqr(x96) =G= 0.8836;

e138.. sqr(x83) + sqr(x97) =G= 0.8836;

e139.. sqr(x84) + sqr(x98) =G= 0.8836;

e140.. sqr(x85) + sqr(x99) =G= 0.8836;

e141.. sqr(x86) + sqr(x100) =G= 0.8836;

e142.. sqr(x87) + sqr(x101) =G= 0.8836;

e143.. sqr(x88) + sqr(x102) =G= 0.8836;

e144.. sqr(x89) + sqr(x103) =G= 0.8836;

e145.. sqr(x90) + sqr(x104) =G= 0.8836;

e146.. sqr(x91) + sqr(x105) =G= 0.8836;

e147.. sqr(x92) + sqr(x106) =G= 0.8836;

e148.. sqr(x93) + sqr(x107) =G= 0.8836;

e149.. sqr(x94) + sqr(x108) =G= 0.8836;

e150..    x109 =L= 3.324;

e151..    x110 =L= 1.4;

e152..    x111 =L= 1;

e153..    x112 =L= 1;

e154..    x113 =L= 1;

e155..    x109 =G= 0;

e156..    x110 =G= 0;

e157..    x111 =G= 0;

e158..    x112 =G= 0;

e159..    x113 =G= 0;

e160..    x114 =L= 0.1;

e161..    x115 =L= 0.5;

e162..    x116 =L= 0.4;

e163..    x117 =L= 0.24;

e164..    x118 =L= 0.24;

e165..    x114 =G= 0;

e166..    x115 =G= -0.4;

e167..    x116 =G= 0;

e168..    x117 =G= -0.06;

e169..    x118 =G= -0.06;

e170..    x95 =E= 0;

e171..    x27 + x31 - x109 =E= 0;

e172..    x1 + x32 + x33 + x39 - x110 =E= -0.217;

e173..    x2 + x35 - x111 =E= -0.942;

e174..    x10 + x15 + x21 + x23 - x112 =E= -0.112;

e175..    x18 - x113 =E= 0;

e176..    x67 + x71 - x114 =E= 0;

e177..    x41 + x72 + x73 + x79 - x115 =E= -0.127;

e178..    x42 + x75 - x116 =E= -0.19;

e179..    x50 + x55 + x61 + x63 - x117 =E= -0.075;

e180..    x58 - x118 =E= 0;

e181..    x7 + x13 + x36 + x37 + x40 =E= -0.478;

e182..    x9 + x14 + x28 + x34 =E= -0.076;

e183..    x3 + x8 + x17 =E= 0;

e184..    x4 + x11 + x29 + x38 =E= -0.295;

e185..    x5 + x30 =E= -0.09;

e186..    x6 + x24 =E= -0.035;

e187..    x22 + x25 =E= -0.061;

e188..    x16 + x19 + x26 =E= -0.135;

e189..    x12 + x20 =E= -0.149;

e190..    x47 + x53 + x76 + x77 + x80 =E= 0.039;

e191..    x49 + x54 + x68 + x74 =E= -0.016;

e192..    x43 + x48 + x57 =E= 0;

e193..    x44 + x51 + x69 + x78 =E= -0.166;

e194..    x45 + x70 =E= -0.058;

e195..    x46 + x64 =E= -0.018;

e196..    x62 + x65 =E= -0.016;

e197..    x56 + x59 + x66 =E= -0.058;

e198..    x52 + x60 =E= -0.05;

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: 2019-11-29 Git hash: 4a97e4ed
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