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Instance p_ball_10b_5p_3d_h

Select 5-points in 3-dimensional balls, such that the l1-distance between all points is minimized.
Only one point can be assigned to each ball, and in total there are 10 balls with radius one.
This is a convex-hull formulation.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
44.00421681 p1 ( gdx sol )
(infeas: 7e-13)
Other points (infeas > 1e-08)  
Dual Bounds
44.00117376 (ALPHAECP)
44.00421676 (ANTIGONE)
44.00417902 (BARON)
44.00421679 (BONMIN)
44.00419481 (COUENNE)
44.00421680 (LINDO)
44.00421325 (SCIP)
0.00000000 (SHOT)
References Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020.
Source p_ball_10b_5p_3d_H.gms with the epsilon in the perspective formulation changed to 1e-4, contributed by Jan Kronqvist and Ruth Misener
Application Geometry
Added to library 26 Aug 2020
Problem type MBNLP
#Variables 245
#Binary Variables 50
#Integer Variables 0
#Nonlinear Variables 200
#Nonlinear Binary Variables 50
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 30
#Nonlinear Nonzeros in Objective 0
#Constraints 294
#Linear Constraints 244
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 50
Operands in Gen. Nonlin. Functions div mul sqr
Constraints curvature convex
#Nonzeros in Jacobian 953
#Nonlinear Nonzeros in Jacobian 200
#Nonzeros in (Upper-Left) Hessian of Lagrangian 500
#Nonzeros in Diagonal of Hessian of Lagrangian 200
#Blocks in Hessian of Lagrangian 50
Minimal blocksize in Hessian of Lagrangian 4
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 4.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-04
Maximal coefficient 1.0000e+01
Infeasibility of initial point 1
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
*        295       21        0      274        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        246      196       50        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        984      784      200        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
          ,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,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
          ,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155
          ,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167,x168
          ,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180,x181
          ,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192,x193,x194
          ,x195,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205,x206,x207
          ,x208,x209,x210,x211,x212,x213,x214,x215,x216,x217,x218,x219,x220
          ,x221,x222,x223,x224,x225,x226,x227,x228,x229,x230,x231,x232,x233
          ,x234,x235,x236,x237,x238,x239,x240,x241,x242,x243,x244,x245,objvar;

Positive Variables  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,x143,x144,x145,x146,x147,x148,x149,x150
          ,x151,x152,x153,x154,x155,x156,x157,x158,x159,x160,x161,x162,x163
          ,x164,x165,x166,x167,x168,x169,x170,x171,x172,x173,x174,x175,x176
          ,x177,x178,x179,x180,x181,x182,x183,x184,x185,x186,x187,x188,x189
          ,x190,x191,x192,x193,x194,x195,x196,x197,x198,x199,x200,x201,x202
          ,x203,x204,x205,x206,x207,x208,x209,x210,x211,x212,x213,x214,x215
          ,x216,x217,x218,x219,x220,x221,x222,x223,x224,x225,x226,x227,x228
          ,x229,x230,x231,x232,x233,x234,x235,x236,x237,x238,x239,x240,x241
          ,x242,x243,x244,x245;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
          ,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
          ,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50;

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,e199,e200,e201,e202,e203,e204,e205,e206,e207
          ,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
          ,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
          ,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
          ,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
          ,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
          ,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
          ,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295;


e1..    x51 - x52 - x53 =L= 0;

e2..  - x51 + x52 - x53 =L= 0;

e3..    x54 - x55 - x56 =L= 0;

e4..  - x54 + x55 - x56 =L= 0;

e5..    x57 - x58 - x59 =L= 0;

e6..  - x57 + x58 - x59 =L= 0;

e7..    x51 - x60 - x61 =L= 0;

e8..  - x51 + x60 - x61 =L= 0;

e9..    x54 - x62 - x63 =L= 0;

e10..  - x54 + x62 - x63 =L= 0;

e11..    x57 - x64 - x65 =L= 0;

e12..  - x57 + x64 - x65 =L= 0;

e13..    x51 - x66 - x67 =L= 0;

e14..  - x51 + x66 - x67 =L= 0;

e15..    x54 - x68 - x69 =L= 0;

e16..  - x54 + x68 - x69 =L= 0;

e17..    x57 - x70 - x71 =L= 0;

e18..  - x57 + x70 - x71 =L= 0;

e19..    x51 - x72 - x73 =L= 0;

e20..  - x51 + x72 - x73 =L= 0;

e21..    x54 - x74 - x75 =L= 0;

e22..  - x54 + x74 - x75 =L= 0;

e23..    x57 - x76 - x77 =L= 0;

e24..  - x57 + x76 - x77 =L= 0;

e25..    x52 - x60 - x78 =L= 0;

e26..  - x52 + x60 - x78 =L= 0;

e27..    x55 - x62 - x79 =L= 0;

e28..  - x55 + x62 - x79 =L= 0;

e29..    x58 - x64 - x80 =L= 0;

e30..  - x58 + x64 - x80 =L= 0;

e31..    x52 - x66 - x81 =L= 0;

e32..  - x52 + x66 - x81 =L= 0;

e33..    x55 - x68 - x82 =L= 0;

e34..  - x55 + x68 - x82 =L= 0;

e35..    x58 - x70 - x83 =L= 0;

e36..  - x58 + x70 - x83 =L= 0;

e37..    x52 - x72 - x84 =L= 0;

e38..  - x52 + x72 - x84 =L= 0;

e39..    x55 - x74 - x85 =L= 0;

e40..  - x55 + x74 - x85 =L= 0;

e41..    x58 - x76 - x86 =L= 0;

e42..  - x58 + x76 - x86 =L= 0;

e43..    x60 - x66 - x87 =L= 0;

e44..  - x60 + x66 - x87 =L= 0;

e45..    x62 - x68 - x88 =L= 0;

e46..  - x62 + x68 - x88 =L= 0;

e47..    x64 - x70 - x89 =L= 0;

e48..  - x64 + x70 - x89 =L= 0;

e49..    x60 - x72 - x90 =L= 0;

e50..  - x60 + x72 - x90 =L= 0;

e51..    x62 - x74 - x91 =L= 0;

e52..  - x62 + x74 - x91 =L= 0;

e53..    x64 - x76 - x92 =L= 0;

e54..  - x64 + x76 - x92 =L= 0;

e55..    x66 - x72 - x93 =L= 0;

e56..  - x66 + x72 - x93 =L= 0;

e57..    x68 - x74 - x94 =L= 0;

e58..  - x68 + x74 - x94 =L= 0;

e59..    x70 - x76 - x95 =L= 0;

e60..  - x70 + x76 - x95 =L= 0;

e61.. (-1 + sqr(3.55441530772447 - x96/(0.0001 + 0.9999*b1)) + sqr(
      2.6588399811956 - x97/(0.0001 + 0.9999*b1)) + sqr(5.16713392802669 - x98/
      (0.0001 + 0.9999*b1)))*(0.0001 + 0.9999*b1) + 0.00454025712555548*b1
       =L= 0.00454025712555548;

e62.. (-1 + sqr(8.82094045941646 - x99/(0.0001 + 0.9999*b2)) + sqr(
      9.51816335093057 - x100/(0.0001 + 0.9999*b2)) + sqr(0.894770759747333 - 
      x101/(0.0001 + 0.9999*b2)))*(0.0001 + 0.9999*b2) + 0.0168205038876067*b2
       =L= 0.0168205038876067;

e63.. (-1 + sqr(6.86229591973038 - x102/(0.0001 + 0.9999*b3)) + sqr(
      4.74665709736901 - x103/(0.0001 + 0.9999*b3)) + sqr(1.14651582775383 - 
      x104/(0.0001 + 0.9999*b3)))*(0.0001 + 0.9999*b3) + 0.0069936357433242*b3
       =L= 0.0069936357433242;

e64.. (-1 + sqr(7.13880287505566 - x105/(0.0001 + 0.9999*b4)) + sqr(
      0.923639199248324 - x106/(0.0001 + 0.9999*b4)) + sqr(5.06906794010293 - 
      x107/(0.0001 + 0.9999*b4)))*(0.0001 + 0.9999*b4) + 0.00765110656406704*b4
       =L= 0.00765110656406704;

e65.. (-1 + sqr(9.54873475130122 - x108/(0.0001 + 0.9999*b5)) + sqr(
      9.730708594994 - x109/(0.0001 + 0.9999*b5)) + sqr(0.506682101270036 - 
      x110/(0.0001 + 0.9999*b5)))*(0.0001 + 0.9999*b5) + 0.0185121751863145*b5
       =L= 0.0185121751863145;

e66.. (-1 + sqr(2.60295575976191 - x111/(0.0001 + 0.9999*b6)) + sqr(
      9.60525309364094 - x112/(0.0001 + 0.9999*b6)) + sqr(5.33059723504087 - 
      x113/(0.0001 + 0.9999*b6)))*(0.0001 + 0.9999*b6) + 0.0126451532562402*b6
       =L= 0.0126451532562402;

e67.. (-1 + sqr(8.7489239697277 - x114/(0.0001 + 0.9999*b7)) + sqr(
      6.42418905563567 - x115/(0.0001 + 0.9999*b7)) + sqr(6.53764526999883 - 
      x116/(0.0001 + 0.9999*b7)))*(0.0001 + 0.9999*b7) + 0.0159554681326963*b7
       =L= 0.0159554681326963;

e68.. (-1 + sqr(2.98069751112782 - x117/(0.0001 + 0.9999*b8)) + sqr(
      1.4913715136506 - x118/(0.0001 + 0.9999*b8)) + sqr(2.04987567063475 - 
      x119/(0.0001 + 0.9999*b8)))*(0.0001 + 0.9999*b8) + 0.00143107369096323*b8
       =L= 0.00143107369096323;

e69.. (-1 + sqr(1.65791995565741 - x120/(0.0001 + 0.9999*b9)) + sqr(
      6.17322651944292 - x121/(0.0001 + 0.9999*b9)) + sqr(7.01412219987569 - 
      x122/(0.0001 + 0.9999*b9)))*(0.0001 + 0.9999*b9) + 0.00890553344745093*b9
       =L= 0.00890553344745093;

e70.. (-1 + sqr(2.41953526971379 - x123/(0.0001 + 0.9999*b10)) + sqr(
      1.09500973629707 - x124/(0.0001 + 0.9999*b10)) + sqr(2.60189595048839 - 
      x125/(0.0001 + 0.9999*b10)))*(0.0001 + 0.9999*b10) + 0.00128230597811422*
      b10 =L= 0.00128230597811422;

e71..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 =E= 1;

e72.. (-1 + sqr(3.55441530772447 - x126/(0.0001 + 0.9999*b11)) + sqr(
      2.6588399811956 - x127/(0.0001 + 0.9999*b11)) + sqr(5.16713392802669 - 
      x128/(0.0001 + 0.9999*b11)))*(0.0001 + 0.9999*b11) + 0.00454025712555548*
      b11 =L= 0.00454025712555548;

e73.. (-1 + sqr(8.82094045941646 - x129/(0.0001 + 0.9999*b12)) + sqr(
      9.51816335093057 - x130/(0.0001 + 0.9999*b12)) + sqr(0.894770759747333 - 
      x131/(0.0001 + 0.9999*b12)))*(0.0001 + 0.9999*b12) + 0.0168205038876067*
      b12 =L= 0.0168205038876067;

e74.. (-1 + sqr(6.86229591973038 - x132/(0.0001 + 0.9999*b13)) + sqr(
      4.74665709736901 - x133/(0.0001 + 0.9999*b13)) + sqr(1.14651582775383 - 
      x134/(0.0001 + 0.9999*b13)))*(0.0001 + 0.9999*b13) + 0.0069936357433242*
      b13 =L= 0.0069936357433242;

e75.. (-1 + sqr(7.13880287505566 - x135/(0.0001 + 0.9999*b14)) + sqr(
      0.923639199248324 - x136/(0.0001 + 0.9999*b14)) + sqr(5.06906794010293 - 
      x137/(0.0001 + 0.9999*b14)))*(0.0001 + 0.9999*b14) + 0.00765110656406704*
      b14 =L= 0.00765110656406704;

e76.. (-1 + sqr(9.54873475130122 - x138/(0.0001 + 0.9999*b15)) + sqr(
      9.730708594994 - x139/(0.0001 + 0.9999*b15)) + sqr(0.506682101270036 - 
      x140/(0.0001 + 0.9999*b15)))*(0.0001 + 0.9999*b15) + 0.0185121751863145*
      b15 =L= 0.0185121751863145;

e77.. (-1 + sqr(2.60295575976191 - x141/(0.0001 + 0.9999*b16)) + sqr(
      9.60525309364094 - x142/(0.0001 + 0.9999*b16)) + sqr(5.33059723504087 - 
      x143/(0.0001 + 0.9999*b16)))*(0.0001 + 0.9999*b16) + 0.0126451532562402*
      b16 =L= 0.0126451532562402;

e78.. (-1 + sqr(8.7489239697277 - x144/(0.0001 + 0.9999*b17)) + sqr(
      6.42418905563567 - x145/(0.0001 + 0.9999*b17)) + sqr(6.53764526999883 - 
      x146/(0.0001 + 0.9999*b17)))*(0.0001 + 0.9999*b17) + 0.0159554681326963*
      b17 =L= 0.0159554681326963;

e79.. (-1 + sqr(2.98069751112782 - x147/(0.0001 + 0.9999*b18)) + sqr(
      1.4913715136506 - x148/(0.0001 + 0.9999*b18)) + sqr(2.04987567063475 - 
      x149/(0.0001 + 0.9999*b18)))*(0.0001 + 0.9999*b18) + 0.00143107369096323*
      b18 =L= 0.00143107369096323;

e80.. (-1 + sqr(1.65791995565741 - x150/(0.0001 + 0.9999*b19)) + sqr(
      6.17322651944292 - x151/(0.0001 + 0.9999*b19)) + sqr(7.01412219987569 - 
      x152/(0.0001 + 0.9999*b19)))*(0.0001 + 0.9999*b19) + 0.00890553344745093*
      b19 =L= 0.00890553344745093;

e81.. (-1 + sqr(2.41953526971379 - x153/(0.0001 + 0.9999*b20)) + sqr(
      1.09500973629707 - x154/(0.0001 + 0.9999*b20)) + sqr(2.60189595048839 - 
      x155/(0.0001 + 0.9999*b20)))*(0.0001 + 0.9999*b20) + 0.00128230597811422*
      b20 =L= 0.00128230597811422;

e82..    b11 + b12 + b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;

e83.. (-1 + sqr(3.55441530772447 - x156/(0.0001 + 0.9999*b21)) + sqr(
      2.6588399811956 - x157/(0.0001 + 0.9999*b21)) + sqr(5.16713392802669 - 
      x158/(0.0001 + 0.9999*b21)))*(0.0001 + 0.9999*b21) + 0.00454025712555548*
      b21 =L= 0.00454025712555548;

e84.. (-1 + sqr(8.82094045941646 - x159/(0.0001 + 0.9999*b22)) + sqr(
      9.51816335093057 - x160/(0.0001 + 0.9999*b22)) + sqr(0.894770759747333 - 
      x161/(0.0001 + 0.9999*b22)))*(0.0001 + 0.9999*b22) + 0.0168205038876067*
      b22 =L= 0.0168205038876067;

e85.. (-1 + sqr(6.86229591973038 - x162/(0.0001 + 0.9999*b23)) + sqr(
      4.74665709736901 - x163/(0.0001 + 0.9999*b23)) + sqr(1.14651582775383 - 
      x164/(0.0001 + 0.9999*b23)))*(0.0001 + 0.9999*b23) + 0.0069936357433242*
      b23 =L= 0.0069936357433242;

e86.. (-1 + sqr(7.13880287505566 - x165/(0.0001 + 0.9999*b24)) + sqr(
      0.923639199248324 - x166/(0.0001 + 0.9999*b24)) + sqr(5.06906794010293 - 
      x167/(0.0001 + 0.9999*b24)))*(0.0001 + 0.9999*b24) + 0.00765110656406704*
      b24 =L= 0.00765110656406704;

e87.. (-1 + sqr(9.54873475130122 - x168/(0.0001 + 0.9999*b25)) + sqr(
      9.730708594994 - x169/(0.0001 + 0.9999*b25)) + sqr(0.506682101270036 - 
      x170/(0.0001 + 0.9999*b25)))*(0.0001 + 0.9999*b25) + 0.0185121751863145*
      b25 =L= 0.0185121751863145;

e88.. (-1 + sqr(2.60295575976191 - x171/(0.0001 + 0.9999*b26)) + sqr(
      9.60525309364094 - x172/(0.0001 + 0.9999*b26)) + sqr(5.33059723504087 - 
      x173/(0.0001 + 0.9999*b26)))*(0.0001 + 0.9999*b26) + 0.0126451532562402*
      b26 =L= 0.0126451532562402;

e89.. (-1 + sqr(8.7489239697277 - x174/(0.0001 + 0.9999*b27)) + sqr(
      6.42418905563567 - x175/(0.0001 + 0.9999*b27)) + sqr(6.53764526999883 - 
      x176/(0.0001 + 0.9999*b27)))*(0.0001 + 0.9999*b27) + 0.0159554681326963*
      b27 =L= 0.0159554681326963;

e90.. (-1 + sqr(2.98069751112782 - x177/(0.0001 + 0.9999*b28)) + sqr(
      1.4913715136506 - x178/(0.0001 + 0.9999*b28)) + sqr(2.04987567063475 - 
      x179/(0.0001 + 0.9999*b28)))*(0.0001 + 0.9999*b28) + 0.00143107369096323*
      b28 =L= 0.00143107369096323;

e91.. (-1 + sqr(1.65791995565741 - x180/(0.0001 + 0.9999*b29)) + sqr(
      6.17322651944292 - x181/(0.0001 + 0.9999*b29)) + sqr(7.01412219987569 - 
      x182/(0.0001 + 0.9999*b29)))*(0.0001 + 0.9999*b29) + 0.00890553344745093*
      b29 =L= 0.00890553344745093;

e92.. (-1 + sqr(2.41953526971379 - x183/(0.0001 + 0.9999*b30)) + sqr(
      1.09500973629707 - x184/(0.0001 + 0.9999*b30)) + sqr(2.60189595048839 - 
      x185/(0.0001 + 0.9999*b30)))*(0.0001 + 0.9999*b30) + 0.00128230597811422*
      b30 =L= 0.00128230597811422;

e93..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =E= 1;

e94.. (-1 + sqr(3.55441530772447 - x186/(0.0001 + 0.9999*b31)) + sqr(
      2.6588399811956 - x187/(0.0001 + 0.9999*b31)) + sqr(5.16713392802669 - 
      x188/(0.0001 + 0.9999*b31)))*(0.0001 + 0.9999*b31) + 0.00454025712555548*
      b31 =L= 0.00454025712555548;

e95.. (-1 + sqr(8.82094045941646 - x189/(0.0001 + 0.9999*b32)) + sqr(
      9.51816335093057 - x190/(0.0001 + 0.9999*b32)) + sqr(0.894770759747333 - 
      x191/(0.0001 + 0.9999*b32)))*(0.0001 + 0.9999*b32) + 0.0168205038876067*
      b32 =L= 0.0168205038876067;

e96.. (-1 + sqr(6.86229591973038 - x192/(0.0001 + 0.9999*b33)) + sqr(
      4.74665709736901 - x193/(0.0001 + 0.9999*b33)) + sqr(1.14651582775383 - 
      x194/(0.0001 + 0.9999*b33)))*(0.0001 + 0.9999*b33) + 0.0069936357433242*
      b33 =L= 0.0069936357433242;

e97.. (-1 + sqr(7.13880287505566 - x195/(0.0001 + 0.9999*b34)) + sqr(
      0.923639199248324 - x196/(0.0001 + 0.9999*b34)) + sqr(5.06906794010293 - 
      x197/(0.0001 + 0.9999*b34)))*(0.0001 + 0.9999*b34) + 0.00765110656406704*
      b34 =L= 0.00765110656406704;

e98.. (-1 + sqr(9.54873475130122 - x198/(0.0001 + 0.9999*b35)) + sqr(
      9.730708594994 - x199/(0.0001 + 0.9999*b35)) + sqr(0.506682101270036 - 
      x200/(0.0001 + 0.9999*b35)))*(0.0001 + 0.9999*b35) + 0.0185121751863145*
      b35 =L= 0.0185121751863145;

e99.. (-1 + sqr(2.60295575976191 - x201/(0.0001 + 0.9999*b36)) + sqr(
      9.60525309364094 - x202/(0.0001 + 0.9999*b36)) + sqr(5.33059723504087 - 
      x203/(0.0001 + 0.9999*b36)))*(0.0001 + 0.9999*b36) + 0.0126451532562402*
      b36 =L= 0.0126451532562402;

e100.. (-1 + sqr(8.7489239697277 - x204/(0.0001 + 0.9999*b37)) + sqr(
       6.42418905563567 - x205/(0.0001 + 0.9999*b37)) + sqr(6.53764526999883 - 
       x206/(0.0001 + 0.9999*b37)))*(0.0001 + 0.9999*b37) + 0.0159554681326963*
       b37 =L= 0.0159554681326963;

e101.. (-1 + sqr(2.98069751112782 - x207/(0.0001 + 0.9999*b38)) + sqr(
       1.4913715136506 - x208/(0.0001 + 0.9999*b38)) + sqr(2.04987567063475 - 
       x209/(0.0001 + 0.9999*b38)))*(0.0001 + 0.9999*b38) + 0.00143107369096323
       *b38 =L= 0.00143107369096323;

e102.. (-1 + sqr(1.65791995565741 - x210/(0.0001 + 0.9999*b39)) + sqr(
       6.17322651944292 - x211/(0.0001 + 0.9999*b39)) + sqr(7.01412219987569 - 
       x212/(0.0001 + 0.9999*b39)))*(0.0001 + 0.9999*b39) + 0.00890553344745093
       *b39 =L= 0.00890553344745093;

e103.. (-1 + sqr(2.41953526971379 - x213/(0.0001 + 0.9999*b40)) + sqr(
       1.09500973629707 - x214/(0.0001 + 0.9999*b40)) + sqr(2.60189595048839 - 
       x215/(0.0001 + 0.9999*b40)))*(0.0001 + 0.9999*b40) + 0.00128230597811422
       *b40 =L= 0.00128230597811422;

e104..    b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e105.. (-1 + sqr(3.55441530772447 - x216/(0.0001 + 0.9999*b41)) + sqr(
       2.6588399811956 - x217/(0.0001 + 0.9999*b41)) + sqr(5.16713392802669 - 
       x218/(0.0001 + 0.9999*b41)))*(0.0001 + 0.9999*b41) + 0.00454025712555548
       *b41 =L= 0.00454025712555548;

e106.. (-1 + sqr(8.82094045941646 - x219/(0.0001 + 0.9999*b42)) + sqr(
       9.51816335093057 - x220/(0.0001 + 0.9999*b42)) + sqr(0.894770759747333
        - x221/(0.0001 + 0.9999*b42)))*(0.0001 + 0.9999*b42) + 
       0.0168205038876067*b42 =L= 0.0168205038876067;

e107.. (-1 + sqr(6.86229591973038 - x222/(0.0001 + 0.9999*b43)) + sqr(
       4.74665709736901 - x223/(0.0001 + 0.9999*b43)) + sqr(1.14651582775383 - 
       x224/(0.0001 + 0.9999*b43)))*(0.0001 + 0.9999*b43) + 0.0069936357433242*
       b43 =L= 0.0069936357433242;

e108.. (-1 + sqr(7.13880287505566 - x225/(0.0001 + 0.9999*b44)) + sqr(
       0.923639199248324 - x226/(0.0001 + 0.9999*b44)) + sqr(5.06906794010293
        - x227/(0.0001 + 0.9999*b44)))*(0.0001 + 0.9999*b44) + 
       0.00765110656406704*b44 =L= 0.00765110656406704;

e109.. (-1 + sqr(9.54873475130122 - x228/(0.0001 + 0.9999*b45)) + sqr(
       9.730708594994 - x229/(0.0001 + 0.9999*b45)) + sqr(0.506682101270036 - 
       x230/(0.0001 + 0.9999*b45)))*(0.0001 + 0.9999*b45) + 0.0185121751863145*
       b45 =L= 0.0185121751863145;

e110.. (-1 + sqr(2.60295575976191 - x231/(0.0001 + 0.9999*b46)) + sqr(
       9.60525309364094 - x232/(0.0001 + 0.9999*b46)) + sqr(5.33059723504087 - 
       x233/(0.0001 + 0.9999*b46)))*(0.0001 + 0.9999*b46) + 0.0126451532562402*
       b46 =L= 0.0126451532562402;

e111.. (-1 + sqr(8.7489239697277 - x234/(0.0001 + 0.9999*b47)) + sqr(
       6.42418905563567 - x235/(0.0001 + 0.9999*b47)) + sqr(6.53764526999883 - 
       x236/(0.0001 + 0.9999*b47)))*(0.0001 + 0.9999*b47) + 0.0159554681326963*
       b47 =L= 0.0159554681326963;

e112.. (-1 + sqr(2.98069751112782 - x237/(0.0001 + 0.9999*b48)) + sqr(
       1.4913715136506 - x238/(0.0001 + 0.9999*b48)) + sqr(2.04987567063475 - 
       x239/(0.0001 + 0.9999*b48)))*(0.0001 + 0.9999*b48) + 0.00143107369096323
       *b48 =L= 0.00143107369096323;

e113.. (-1 + sqr(1.65791995565741 - x240/(0.0001 + 0.9999*b49)) + sqr(
       6.17322651944292 - x241/(0.0001 + 0.9999*b49)) + sqr(7.01412219987569 - 
       x242/(0.0001 + 0.9999*b49)))*(0.0001 + 0.9999*b49) + 0.00890553344745093
       *b49 =L= 0.00890553344745093;

e114.. (-1 + sqr(2.41953526971379 - x243/(0.0001 + 0.9999*b50)) + sqr(
       1.09500973629707 - x244/(0.0001 + 0.9999*b50)) + sqr(2.60189595048839 - 
       x245/(0.0001 + 0.9999*b50)))*(0.0001 + 0.9999*b50) + 0.00128230597811422
       *b50 =L= 0.00128230597811422;

e115..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 =E= 1;

e116..    b1 + b11 + b21 + b31 + b41 =L= 1;

e117..    b2 + b12 + b22 + b32 + b42 =L= 1;

e118..    b3 + b13 + b23 + b33 + b43 =L= 1;

e119..    b4 + b14 + b24 + b34 + b44 =L= 1;

e120..    b5 + b15 + b25 + b35 + b45 =L= 1;

e121..    b6 + b16 + b26 + b36 + b46 =L= 1;

e122..    b7 + b17 + b27 + b37 + b47 =L= 1;

e123..    b8 + b18 + b28 + b38 + b48 =L= 1;

e124..    b9 + b19 + b29 + b39 + b49 =L= 1;

e125..    b10 + b20 + b30 + b40 + b50 =L= 1;

e126..  - x51 + x96 + x99 + x102 + x105 + x108 + x111 + x114 + x117 + x120
        + x123 =E= 0;

e127..  - x54 + x97 + x100 + x103 + x106 + x109 + x112 + x115 + x118 + x121
        + x124 =E= 0;

e128..  - x57 + x98 + x101 + x104 + x107 + x110 + x113 + x116 + x119 + x122
        + x125 =E= 0;

e129..  - x52 + x126 + x129 + x132 + x135 + x138 + x141 + x144 + x147 + x150
        + x153 =E= 0;

e130..  - x55 + x127 + x130 + x133 + x136 + x139 + x142 + x145 + x148 + x151
        + x154 =E= 0;

e131..  - x58 + x128 + x131 + x134 + x137 + x140 + x143 + x146 + x149 + x152
        + x155 =E= 0;

e132..  - x60 + x156 + x159 + x162 + x165 + x168 + x171 + x174 + x177 + x180
        + x183 =E= 0;

e133..  - x62 + x157 + x160 + x163 + x166 + x169 + x172 + x175 + x178 + x181
        + x184 =E= 0;

e134..  - x64 + x158 + x161 + x164 + x167 + x170 + x173 + x176 + x179 + x182
        + x185 =E= 0;

e135..  - x66 + x186 + x189 + x192 + x195 + x198 + x201 + x204 + x207 + x210
        + x213 =E= 0;

e136..  - x68 + x187 + x190 + x193 + x196 + x199 + x202 + x205 + x208 + x211
        + x214 =E= 0;

e137..  - x70 + x188 + x191 + x194 + x197 + x200 + x203 + x206 + x209 + x212
        + x215 =E= 0;

e138..  - x72 + x216 + x219 + x222 + x225 + x228 + x231 + x234 + x237 + x240
        + x243 =E= 0;

e139..  - x74 + x217 + x220 + x223 + x226 + x229 + x232 + x235 + x238 + x241
        + x244 =E= 0;

e140..  - x76 + x218 + x221 + x224 + x227 + x230 + x233 + x236 + x239 + x242
        + x245 =E= 0;

e141..  - 10*b1 + x96 =L= 0;

e142..  - 10*b2 + x99 =L= 0;

e143..  - 10*b3 + x102 =L= 0;

e144..  - 10*b4 + x105 =L= 0;

e145..  - 10*b5 + x108 =L= 0;

e146..  - 10*b6 + x111 =L= 0;

e147..  - 10*b7 + x114 =L= 0;

e148..  - 10*b8 + x117 =L= 0;

e149..  - 10*b9 + x120 =L= 0;

e150..  - 10*b10 + x123 =L= 0;

e151..  - 10*b1 + x97 =L= 0;

e152..  - 10*b2 + x100 =L= 0;

e153..  - 10*b3 + x103 =L= 0;

e154..  - 10*b4 + x106 =L= 0;

e155..  - 10*b5 + x109 =L= 0;

e156..  - 10*b6 + x112 =L= 0;

e157..  - 10*b7 + x115 =L= 0;

e158..  - 10*b8 + x118 =L= 0;

e159..  - 10*b9 + x121 =L= 0;

e160..  - 10*b10 + x124 =L= 0;

e161..  - 10*b1 + x98 =L= 0;

e162..  - 10*b2 + x101 =L= 0;

e163..  - 10*b3 + x104 =L= 0;

e164..  - 10*b4 + x107 =L= 0;

e165..  - 10*b5 + x110 =L= 0;

e166..  - 10*b6 + x113 =L= 0;

e167..  - 10*b7 + x116 =L= 0;

e168..  - 10*b8 + x119 =L= 0;

e169..  - 10*b9 + x122 =L= 0;

e170..  - 10*b10 + x125 =L= 0;

e171..  - 10*b11 + x126 =L= 0;

e172..  - 10*b12 + x129 =L= 0;

e173..  - 10*b13 + x132 =L= 0;

e174..  - 10*b14 + x135 =L= 0;

e175..  - 10*b15 + x138 =L= 0;

e176..  - 10*b16 + x141 =L= 0;

e177..  - 10*b17 + x144 =L= 0;

e178..  - 10*b18 + x147 =L= 0;

e179..  - 10*b19 + x150 =L= 0;

e180..  - 10*b20 + x153 =L= 0;

e181..  - 10*b11 + x127 =L= 0;

e182..  - 10*b12 + x130 =L= 0;

e183..  - 10*b13 + x133 =L= 0;

e184..  - 10*b14 + x136 =L= 0;

e185..  - 10*b15 + x139 =L= 0;

e186..  - 10*b16 + x142 =L= 0;

e187..  - 10*b17 + x145 =L= 0;

e188..  - 10*b18 + x148 =L= 0;

e189..  - 10*b19 + x151 =L= 0;

e190..  - 10*b20 + x154 =L= 0;

e191..  - 10*b11 + x128 =L= 0;

e192..  - 10*b12 + x131 =L= 0;

e193..  - 10*b13 + x134 =L= 0;

e194..  - 10*b14 + x137 =L= 0;

e195..  - 10*b15 + x140 =L= 0;

e196..  - 10*b16 + x143 =L= 0;

e197..  - 10*b17 + x146 =L= 0;

e198..  - 10*b18 + x149 =L= 0;

e199..  - 10*b19 + x152 =L= 0;

e200..  - 10*b20 + x155 =L= 0;

e201..  - 10*b21 + x156 =L= 0;

e202..  - 10*b22 + x159 =L= 0;

e203..  - 10*b23 + x162 =L= 0;

e204..  - 10*b24 + x165 =L= 0;

e205..  - 10*b25 + x168 =L= 0;

e206..  - 10*b26 + x171 =L= 0;

e207..  - 10*b27 + x174 =L= 0;

e208..  - 10*b28 + x177 =L= 0;

e209..  - 10*b29 + x180 =L= 0;

e210..  - 10*b30 + x183 =L= 0;

e211..  - 10*b21 + x157 =L= 0;

e212..  - 10*b22 + x160 =L= 0;

e213..  - 10*b23 + x163 =L= 0;

e214..  - 10*b24 + x166 =L= 0;

e215..  - 10*b25 + x169 =L= 0;

e216..  - 10*b26 + x172 =L= 0;

e217..  - 10*b27 + x175 =L= 0;

e218..  - 10*b28 + x178 =L= 0;

e219..  - 10*b29 + x181 =L= 0;

e220..  - 10*b30 + x184 =L= 0;

e221..  - 10*b21 + x158 =L= 0;

e222..  - 10*b22 + x161 =L= 0;

e223..  - 10*b23 + x164 =L= 0;

e224..  - 10*b24 + x167 =L= 0;

e225..  - 10*b25 + x170 =L= 0;

e226..  - 10*b26 + x173 =L= 0;

e227..  - 10*b27 + x176 =L= 0;

e228..  - 10*b28 + x179 =L= 0;

e229..  - 10*b29 + x182 =L= 0;

e230..  - 10*b30 + x185 =L= 0;

e231..  - 10*b31 + x186 =L= 0;

e232..  - 10*b32 + x189 =L= 0;

e233..  - 10*b33 + x192 =L= 0;

e234..  - 10*b34 + x195 =L= 0;

e235..  - 10*b35 + x198 =L= 0;

e236..  - 10*b36 + x201 =L= 0;

e237..  - 10*b37 + x204 =L= 0;

e238..  - 10*b38 + x207 =L= 0;

e239..  - 10*b39 + x210 =L= 0;

e240..  - 10*b40 + x213 =L= 0;

e241..  - 10*b31 + x187 =L= 0;

e242..  - 10*b32 + x190 =L= 0;

e243..  - 10*b33 + x193 =L= 0;

e244..  - 10*b34 + x196 =L= 0;

e245..  - 10*b35 + x199 =L= 0;

e246..  - 10*b36 + x202 =L= 0;

e247..  - 10*b37 + x205 =L= 0;

e248..  - 10*b38 + x208 =L= 0;

e249..  - 10*b39 + x211 =L= 0;

e250..  - 10*b40 + x214 =L= 0;

e251..  - 10*b31 + x188 =L= 0;

e252..  - 10*b32 + x191 =L= 0;

e253..  - 10*b33 + x194 =L= 0;

e254..  - 10*b34 + x197 =L= 0;

e255..  - 10*b35 + x200 =L= 0;

e256..  - 10*b36 + x203 =L= 0;

e257..  - 10*b37 + x206 =L= 0;

e258..  - 10*b38 + x209 =L= 0;

e259..  - 10*b39 + x212 =L= 0;

e260..  - 10*b40 + x215 =L= 0;

e261..  - 10*b41 + x216 =L= 0;

e262..  - 10*b42 + x219 =L= 0;

e263..  - 10*b43 + x222 =L= 0;

e264..  - 10*b44 + x225 =L= 0;

e265..  - 10*b45 + x228 =L= 0;

e266..  - 10*b46 + x231 =L= 0;

e267..  - 10*b47 + x234 =L= 0;

e268..  - 10*b48 + x237 =L= 0;

e269..  - 10*b49 + x240 =L= 0;

e270..  - 10*b50 + x243 =L= 0;

e271..  - 10*b41 + x217 =L= 0;

e272..  - 10*b42 + x220 =L= 0;

e273..  - 10*b43 + x223 =L= 0;

e274..  - 10*b44 + x226 =L= 0;

e275..  - 10*b45 + x229 =L= 0;

e276..  - 10*b46 + x232 =L= 0;

e277..  - 10*b47 + x235 =L= 0;

e278..  - 10*b48 + x238 =L= 0;

e279..  - 10*b49 + x241 =L= 0;

e280..  - 10*b50 + x244 =L= 0;

e281..  - 10*b41 + x218 =L= 0;

e282..  - 10*b42 + x221 =L= 0;

e283..  - 10*b43 + x224 =L= 0;

e284..  - 10*b44 + x227 =L= 0;

e285..  - 10*b45 + x230 =L= 0;

e286..  - 10*b46 + x233 =L= 0;

e287..  - 10*b47 + x236 =L= 0;

e288..  - 10*b48 + x239 =L= 0;

e289..  - 10*b49 + x242 =L= 0;

e290..  - 10*b50 + x245 =L= 0;

e291..    x51 - x52 =L= 0;

e292..    x52 - x60 =L= 0;

e293..    x60 - x66 =L= 0;

e294..    x66 - x72 =L= 0;

e295..  - x53 - x56 - x59 - x61 - x63 - x65 - x67 - x69 - x71 - x73 - x75 - x77
        - x78 - x79 - x80 - x81 - x82 - x83 - x84 - x85 - x86 - x87 - x88 - x89
        - x90 - x91 - x92 - x93 - x94 - x95 + objvar =E= 0;

* set non-default bounds
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 = 10;
x68.up = 10;
x69.up = 10;
x70.up = 10;
x71.up = 10;
x72.up = 10;
x73.up = 10;
x74.up = 10;
x75.up = 10;
x76.up = 10;
x77.up = 10;
x78.up = 10;
x79.up = 10;
x80.up = 10;
x81.up = 10;
x82.up = 10;
x83.up = 10;
x84.up = 10;
x85.up = 10;
x86.up = 10;
x87.up = 10;
x88.up = 10;
x89.up = 10;
x90.up = 10;
x91.up = 10;
x92.up = 10;
x93.up = 10;
x94.up = 10;
x95.up = 10;
x96.up = 10;
x97.up = 10;
x98.up = 10;
x99.up = 10;
x100.up = 10;
x101.up = 10;
x102.up = 10;
x103.up = 10;
x104.up = 10;
x105.up = 10;
x106.up = 10;
x107.up = 10;
x108.up = 10;
x109.up = 10;
x110.up = 10;
x111.up = 10;
x112.up = 10;
x113.up = 10;
x114.up = 10;
x115.up = 10;
x116.up = 10;
x117.up = 10;
x118.up = 10;
x119.up = 10;
x120.up = 10;
x121.up = 10;
x122.up = 10;
x123.up = 10;
x124.up = 10;
x125.up = 10;
x126.up = 10;
x127.up = 10;
x128.up = 10;
x129.up = 10;
x130.up = 10;
x131.up = 10;
x132.up = 10;
x133.up = 10;
x134.up = 10;
x135.up = 10;
x136.up = 10;
x137.up = 10;
x138.up = 10;
x139.up = 10;
x140.up = 10;
x141.up = 10;
x142.up = 10;
x143.up = 10;
x144.up = 10;
x145.up = 10;
x146.up = 10;
x147.up = 10;
x148.up = 10;
x149.up = 10;
x150.up = 10;
x151.up = 10;
x152.up = 10;
x153.up = 10;
x154.up = 10;
x155.up = 10;
x156.up = 10;
x157.up = 10;
x158.up = 10;
x159.up = 10;
x160.up = 10;
x161.up = 10;
x162.up = 10;
x163.up = 10;
x164.up = 10;
x165.up = 10;
x166.up = 10;
x167.up = 10;
x168.up = 10;
x169.up = 10;
x170.up = 10;
x171.up = 10;
x172.up = 10;
x173.up = 10;
x174.up = 10;
x175.up = 10;
x176.up = 10;
x177.up = 10;
x178.up = 10;
x179.up = 10;
x180.up = 10;
x181.up = 10;
x182.up = 10;
x183.up = 10;
x184.up = 10;
x185.up = 10;
x186.up = 10;
x187.up = 10;
x188.up = 10;
x189.up = 10;
x190.up = 10;
x191.up = 10;
x192.up = 10;
x193.up = 10;
x194.up = 10;
x195.up = 10;
x196.up = 10;
x197.up = 10;
x198.up = 10;
x199.up = 10;
x200.up = 10;
x201.up = 10;
x202.up = 10;
x203.up = 10;
x204.up = 10;
x205.up = 10;
x206.up = 10;
x207.up = 10;
x208.up = 10;
x209.up = 10;
x210.up = 10;
x211.up = 10;
x212.up = 10;
x213.up = 10;
x214.up = 10;
x215.up = 10;
x216.up = 10;
x217.up = 10;
x218.up = 10;
x219.up = 10;
x220.up = 10;
x221.up = 10;
x222.up = 10;
x223.up = 10;
x224.up = 10;
x225.up = 10;
x226.up = 10;
x227.up = 10;
x228.up = 10;
x229.up = 10;
x230.up = 10;
x231.up = 10;
x232.up = 10;
x233.up = 10;
x234.up = 10;
x235.up = 10;
x236.up = 10;
x237.up = 10;
x238.up = 10;
x239.up = 10;
x240.up = 10;
x241.up = 10;
x242.up = 10;
x243.up = 10;
x244.up = 10;
x245.up = 10;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
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