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Instance p_ball_10b_5p_2d_h

Select 5-points in 2-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)
18.71857799 p1 ( gdx sol )
(infeas: 1e-15)
Other points (infeas > 1e-08)  
Dual Bounds
18.71835427 (ALPHAECP)
18.71857797 (ANTIGONE)
18.71857003 (BARON)
18.71857797 (BONMIN)
18.71856412 (COUENNE)
18.71857799 (LINDO)
18.71857507 (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_2d_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 180
#Binary Variables 50
#Integer Variables 0
#Nonlinear Variables 150
#Nonlinear Binary Variables 50
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 0
#Constraints 219
#Linear Constraints 169
#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 688
#Nonlinear Nonzeros in Jacobian 150
#Nonzeros in (Upper-Left) Hessian of Lagrangian 350
#Nonzeros in Diagonal of Hessian of Lagrangian 150
#Blocks in Hessian of Lagrangian 50
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#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
*        220       16        0      204        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        181      131       50        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        709      559      150        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,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;

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;


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..    x51 - x57 - x58 =L= 0;

e6..  - x51 + x57 - x58 =L= 0;

e7..    x54 - x59 - x60 =L= 0;

e8..  - x54 + x59 - x60 =L= 0;

e9..    x51 - x61 - x62 =L= 0;

e10..  - x51 + x61 - x62 =L= 0;

e11..    x54 - x63 - x64 =L= 0;

e12..  - x54 + x63 - x64 =L= 0;

e13..    x51 - x65 - x66 =L= 0;

e14..  - x51 + x65 - x66 =L= 0;

e15..    x54 - x67 - x68 =L= 0;

e16..  - x54 + x67 - x68 =L= 0;

e17..    x52 - x57 - x69 =L= 0;

e18..  - x52 + x57 - x69 =L= 0;

e19..    x55 - x59 - x70 =L= 0;

e20..  - x55 + x59 - x70 =L= 0;

e21..    x52 - x61 - x71 =L= 0;

e22..  - x52 + x61 - x71 =L= 0;

e23..    x55 - x63 - x72 =L= 0;

e24..  - x55 + x63 - x72 =L= 0;

e25..    x52 - x65 - x73 =L= 0;

e26..  - x52 + x65 - x73 =L= 0;

e27..    x55 - x67 - x74 =L= 0;

e28..  - x55 + x67 - x74 =L= 0;

e29..    x57 - x61 - x75 =L= 0;

e30..  - x57 + x61 - x75 =L= 0;

e31..    x59 - x63 - x76 =L= 0;

e32..  - x59 + x63 - x76 =L= 0;

e33..    x57 - x65 - x77 =L= 0;

e34..  - x57 + x65 - x77 =L= 0;

e35..    x59 - x67 - x78 =L= 0;

e36..  - x59 + x67 - x78 =L= 0;

e37..    x61 - x65 - x79 =L= 0;

e38..  - x61 + x65 - x79 =L= 0;

e39..    x63 - x67 - x80 =L= 0;

e40..  - x63 + x67 - x80 =L= 0;

e41.. (-1 + sqr(0.648386267690458 - x81/(0.0001 + 0.9999*b1)) + sqr(
      5.34198386756466 - x82/(0.0001 + 0.9999*b1)))*(0.0001 + 0.9999*b1) + 
      0.00279571963934506*b1 =L= 0.00279571963934506;

e42.. (-1 + sqr(0.38028139143083 - x83/(0.0001 + 0.9999*b2)) + sqr(
      4.79200736168083 - x84/(0.0001 + 0.9999*b2)))*(0.0001 + 0.9999*b2) + 
      0.00221079484910719*b2 =L= 0.00221079484910719;

e43.. (-1 + sqr(4.59553989190787 - x85/(0.0001 + 0.9999*b3)) + sqr(
      2.92927044373959 - x86/(0.0001 + 0.9999*b3)))*(0.0001 + 0.9999*b3) + 
      0.00286996122306829*b3 =L= 0.00286996122306829;

e44.. (-1 + sqr(7.79089239319392 - x87/(0.0001 + 0.9999*b4)) + sqr(
      3.09688601355012 - x88/(0.0001 + 0.9999*b4)))*(0.0001 + 0.9999*b4) + 
      0.00692887072632492*b4 =L= 0.00692887072632492;

e45.. (-1 + sqr(2.20597420581599 - x89/(0.0001 + 0.9999*b5)) + sqr(
      0.880296019425143 - x90/(0.0001 + 0.9999*b5)))*(0.0001 + 0.9999*b5) + 
      0.000464124327854123*b5 =L= 0.000464124327854123;

e46.. (-1 + sqr(4.31093077060147 - x91/(0.0001 + 0.9999*b6)) + sqr(
      5.42555328385657 - x92/(0.0001 + 0.9999*b6)))*(0.0001 + 0.9999*b6) + 
      0.00470207525448854*b6 =L= 0.00470207525448854;

e47.. (-1 + sqr(8.68776252232421 - x93/(0.0001 + 0.9999*b7)) + sqr(
      7.42106012944621 - x94/(0.0001 + 0.9999*b7)))*(0.0001 + 0.9999*b7) + 
      0.0129549351089157*b7 =L= 0.0129549351089157;

e48.. (-1 + sqr(3.86794113528858 - x95/(0.0001 + 0.9999*b8)) + sqr(
      9.34863265837716 - x96/(0.0001 + 0.9999*b8)))*(0.0001 + 0.9999*b8) + 
      0.0101357901207334*b8 =L= 0.0101357901207334;

e49.. (-1 + sqr(8.94294324678777 - x97/(0.0001 + 0.9999*b9)) + sqr(
      0.712193380632226 - x98/(0.0001 + 0.9999*b9)))*(0.0001 + 0.9999*b9) + 
      0.00794834533266834*b9 =L= 0.00794834533266834;

e50.. (-1 + sqr(1.56734614217404 - x99/(0.0001 + 0.9999*b10)) + sqr(
      5.6469805099144 - x100/(0.0001 + 0.9999*b10)))*(0.0001 + 0.9999*b10) + 
      0.00333449628087409*b10 =L= 0.00333449628087409;

e51..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 =E= 1;

e52.. (-1 + sqr(0.648386267690458 - x101/(0.0001 + 0.9999*b11)) + sqr(
      5.34198386756466 - x102/(0.0001 + 0.9999*b11)))*(0.0001 + 0.9999*b11) + 
      0.00279571963934506*b11 =L= 0.00279571963934506;

e53.. (-1 + sqr(0.38028139143083 - x103/(0.0001 + 0.9999*b12)) + sqr(
      4.79200736168083 - x104/(0.0001 + 0.9999*b12)))*(0.0001 + 0.9999*b12) + 
      0.00221079484910719*b12 =L= 0.00221079484910719;

e54.. (-1 + sqr(4.59553989190787 - x105/(0.0001 + 0.9999*b13)) + sqr(
      2.92927044373959 - x106/(0.0001 + 0.9999*b13)))*(0.0001 + 0.9999*b13) + 
      0.00286996122306829*b13 =L= 0.00286996122306829;

e55.. (-1 + sqr(7.79089239319392 - x107/(0.0001 + 0.9999*b14)) + sqr(
      3.09688601355012 - x108/(0.0001 + 0.9999*b14)))*(0.0001 + 0.9999*b14) + 
      0.00692887072632492*b14 =L= 0.00692887072632492;

e56.. (-1 + sqr(2.20597420581599 - x109/(0.0001 + 0.9999*b15)) + sqr(
      0.880296019425143 - x110/(0.0001 + 0.9999*b15)))*(0.0001 + 0.9999*b15) + 
      0.000464124327854123*b15 =L= 0.000464124327854123;

e57.. (-1 + sqr(4.31093077060147 - x111/(0.0001 + 0.9999*b16)) + sqr(
      5.42555328385657 - x112/(0.0001 + 0.9999*b16)))*(0.0001 + 0.9999*b16) + 
      0.00470207525448854*b16 =L= 0.00470207525448854;

e58.. (-1 + sqr(8.68776252232421 - x113/(0.0001 + 0.9999*b17)) + sqr(
      7.42106012944621 - x114/(0.0001 + 0.9999*b17)))*(0.0001 + 0.9999*b17) + 
      0.0129549351089157*b17 =L= 0.0129549351089157;

e59.. (-1 + sqr(3.86794113528858 - x115/(0.0001 + 0.9999*b18)) + sqr(
      9.34863265837716 - x116/(0.0001 + 0.9999*b18)))*(0.0001 + 0.9999*b18) + 
      0.0101357901207334*b18 =L= 0.0101357901207334;

e60.. (-1 + sqr(8.94294324678777 - x117/(0.0001 + 0.9999*b19)) + sqr(
      0.712193380632226 - x118/(0.0001 + 0.9999*b19)))*(0.0001 + 0.9999*b19) + 
      0.00794834533266834*b19 =L= 0.00794834533266834;

e61.. (-1 + sqr(1.56734614217404 - x119/(0.0001 + 0.9999*b20)) + sqr(
      5.6469805099144 - x120/(0.0001 + 0.9999*b20)))*(0.0001 + 0.9999*b20) + 
      0.00333449628087409*b20 =L= 0.00333449628087409;

e62..    b11 + b12 + b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;

e63.. (-1 + sqr(0.648386267690458 - x121/(0.0001 + 0.9999*b21)) + sqr(
      5.34198386756466 - x122/(0.0001 + 0.9999*b21)))*(0.0001 + 0.9999*b21) + 
      0.00279571963934506*b21 =L= 0.00279571963934506;

e64.. (-1 + sqr(0.38028139143083 - x123/(0.0001 + 0.9999*b22)) + sqr(
      4.79200736168083 - x124/(0.0001 + 0.9999*b22)))*(0.0001 + 0.9999*b22) + 
      0.00221079484910719*b22 =L= 0.00221079484910719;

e65.. (-1 + sqr(4.59553989190787 - x125/(0.0001 + 0.9999*b23)) + sqr(
      2.92927044373959 - x126/(0.0001 + 0.9999*b23)))*(0.0001 + 0.9999*b23) + 
      0.00286996122306829*b23 =L= 0.00286996122306829;

e66.. (-1 + sqr(7.79089239319392 - x127/(0.0001 + 0.9999*b24)) + sqr(
      3.09688601355012 - x128/(0.0001 + 0.9999*b24)))*(0.0001 + 0.9999*b24) + 
      0.00692887072632492*b24 =L= 0.00692887072632492;

e67.. (-1 + sqr(2.20597420581599 - x129/(0.0001 + 0.9999*b25)) + sqr(
      0.880296019425143 - x130/(0.0001 + 0.9999*b25)))*(0.0001 + 0.9999*b25) + 
      0.000464124327854123*b25 =L= 0.000464124327854123;

e68.. (-1 + sqr(4.31093077060147 - x131/(0.0001 + 0.9999*b26)) + sqr(
      5.42555328385657 - x132/(0.0001 + 0.9999*b26)))*(0.0001 + 0.9999*b26) + 
      0.00470207525448854*b26 =L= 0.00470207525448854;

e69.. (-1 + sqr(8.68776252232421 - x133/(0.0001 + 0.9999*b27)) + sqr(
      7.42106012944621 - x134/(0.0001 + 0.9999*b27)))*(0.0001 + 0.9999*b27) + 
      0.0129549351089157*b27 =L= 0.0129549351089157;

e70.. (-1 + sqr(3.86794113528858 - x135/(0.0001 + 0.9999*b28)) + sqr(
      9.34863265837716 - x136/(0.0001 + 0.9999*b28)))*(0.0001 + 0.9999*b28) + 
      0.0101357901207334*b28 =L= 0.0101357901207334;

e71.. (-1 + sqr(8.94294324678777 - x137/(0.0001 + 0.9999*b29)) + sqr(
      0.712193380632226 - x138/(0.0001 + 0.9999*b29)))*(0.0001 + 0.9999*b29) + 
      0.00794834533266834*b29 =L= 0.00794834533266834;

e72.. (-1 + sqr(1.56734614217404 - x139/(0.0001 + 0.9999*b30)) + sqr(
      5.6469805099144 - x140/(0.0001 + 0.9999*b30)))*(0.0001 + 0.9999*b30) + 
      0.00333449628087409*b30 =L= 0.00333449628087409;

e73..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =E= 1;

e74.. (-1 + sqr(0.648386267690458 - x141/(0.0001 + 0.9999*b31)) + sqr(
      5.34198386756466 - x142/(0.0001 + 0.9999*b31)))*(0.0001 + 0.9999*b31) + 
      0.00279571963934506*b31 =L= 0.00279571963934506;

e75.. (-1 + sqr(0.38028139143083 - x143/(0.0001 + 0.9999*b32)) + sqr(
      4.79200736168083 - x144/(0.0001 + 0.9999*b32)))*(0.0001 + 0.9999*b32) + 
      0.00221079484910719*b32 =L= 0.00221079484910719;

e76.. (-1 + sqr(4.59553989190787 - x145/(0.0001 + 0.9999*b33)) + sqr(
      2.92927044373959 - x146/(0.0001 + 0.9999*b33)))*(0.0001 + 0.9999*b33) + 
      0.00286996122306829*b33 =L= 0.00286996122306829;

e77.. (-1 + sqr(7.79089239319392 - x147/(0.0001 + 0.9999*b34)) + sqr(
      3.09688601355012 - x148/(0.0001 + 0.9999*b34)))*(0.0001 + 0.9999*b34) + 
      0.00692887072632492*b34 =L= 0.00692887072632492;

e78.. (-1 + sqr(2.20597420581599 - x149/(0.0001 + 0.9999*b35)) + sqr(
      0.880296019425143 - x150/(0.0001 + 0.9999*b35)))*(0.0001 + 0.9999*b35) + 
      0.000464124327854123*b35 =L= 0.000464124327854123;

e79.. (-1 + sqr(4.31093077060147 - x151/(0.0001 + 0.9999*b36)) + sqr(
      5.42555328385657 - x152/(0.0001 + 0.9999*b36)))*(0.0001 + 0.9999*b36) + 
      0.00470207525448854*b36 =L= 0.00470207525448854;

e80.. (-1 + sqr(8.68776252232421 - x153/(0.0001 + 0.9999*b37)) + sqr(
      7.42106012944621 - x154/(0.0001 + 0.9999*b37)))*(0.0001 + 0.9999*b37) + 
      0.0129549351089157*b37 =L= 0.0129549351089157;

e81.. (-1 + sqr(3.86794113528858 - x155/(0.0001 + 0.9999*b38)) + sqr(
      9.34863265837716 - x156/(0.0001 + 0.9999*b38)))*(0.0001 + 0.9999*b38) + 
      0.0101357901207334*b38 =L= 0.0101357901207334;

e82.. (-1 + sqr(8.94294324678777 - x157/(0.0001 + 0.9999*b39)) + sqr(
      0.712193380632226 - x158/(0.0001 + 0.9999*b39)))*(0.0001 + 0.9999*b39) + 
      0.00794834533266834*b39 =L= 0.00794834533266834;

e83.. (-1 + sqr(1.56734614217404 - x159/(0.0001 + 0.9999*b40)) + sqr(
      5.6469805099144 - x160/(0.0001 + 0.9999*b40)))*(0.0001 + 0.9999*b40) + 
      0.00333449628087409*b40 =L= 0.00333449628087409;

e84..    b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e85.. (-1 + sqr(0.648386267690458 - x161/(0.0001 + 0.9999*b41)) + sqr(
      5.34198386756466 - x162/(0.0001 + 0.9999*b41)))*(0.0001 + 0.9999*b41) + 
      0.00279571963934506*b41 =L= 0.00279571963934506;

e86.. (-1 + sqr(0.38028139143083 - x163/(0.0001 + 0.9999*b42)) + sqr(
      4.79200736168083 - x164/(0.0001 + 0.9999*b42)))*(0.0001 + 0.9999*b42) + 
      0.00221079484910719*b42 =L= 0.00221079484910719;

e87.. (-1 + sqr(4.59553989190787 - x165/(0.0001 + 0.9999*b43)) + sqr(
      2.92927044373959 - x166/(0.0001 + 0.9999*b43)))*(0.0001 + 0.9999*b43) + 
      0.00286996122306829*b43 =L= 0.00286996122306829;

e88.. (-1 + sqr(7.79089239319392 - x167/(0.0001 + 0.9999*b44)) + sqr(
      3.09688601355012 - x168/(0.0001 + 0.9999*b44)))*(0.0001 + 0.9999*b44) + 
      0.00692887072632492*b44 =L= 0.00692887072632492;

e89.. (-1 + sqr(2.20597420581599 - x169/(0.0001 + 0.9999*b45)) + sqr(
      0.880296019425143 - x170/(0.0001 + 0.9999*b45)))*(0.0001 + 0.9999*b45) + 
      0.000464124327854123*b45 =L= 0.000464124327854123;

e90.. (-1 + sqr(4.31093077060147 - x171/(0.0001 + 0.9999*b46)) + sqr(
      5.42555328385657 - x172/(0.0001 + 0.9999*b46)))*(0.0001 + 0.9999*b46) + 
      0.00470207525448854*b46 =L= 0.00470207525448854;

e91.. (-1 + sqr(8.68776252232421 - x173/(0.0001 + 0.9999*b47)) + sqr(
      7.42106012944621 - x174/(0.0001 + 0.9999*b47)))*(0.0001 + 0.9999*b47) + 
      0.0129549351089157*b47 =L= 0.0129549351089157;

e92.. (-1 + sqr(3.86794113528858 - x175/(0.0001 + 0.9999*b48)) + sqr(
      9.34863265837716 - x176/(0.0001 + 0.9999*b48)))*(0.0001 + 0.9999*b48) + 
      0.0101357901207334*b48 =L= 0.0101357901207334;

e93.. (-1 + sqr(8.94294324678777 - x177/(0.0001 + 0.9999*b49)) + sqr(
      0.712193380632226 - x178/(0.0001 + 0.9999*b49)))*(0.0001 + 0.9999*b49) + 
      0.00794834533266834*b49 =L= 0.00794834533266834;

e94.. (-1 + sqr(1.56734614217404 - x179/(0.0001 + 0.9999*b50)) + sqr(
      5.6469805099144 - x180/(0.0001 + 0.9999*b50)))*(0.0001 + 0.9999*b50) + 
      0.00333449628087409*b50 =L= 0.00333449628087409;

e95..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 =E= 1;

e96..    b1 + b11 + b21 + b31 + b41 =L= 1;

e97..    b2 + b12 + b22 + b32 + b42 =L= 1;

e98..    b3 + b13 + b23 + b33 + b43 =L= 1;

e99..    b4 + b14 + b24 + b34 + b44 =L= 1;

e100..    b5 + b15 + b25 + b35 + b45 =L= 1;

e101..    b6 + b16 + b26 + b36 + b46 =L= 1;

e102..    b7 + b17 + b27 + b37 + b47 =L= 1;

e103..    b8 + b18 + b28 + b38 + b48 =L= 1;

e104..    b9 + b19 + b29 + b39 + b49 =L= 1;

e105..    b10 + b20 + b30 + b40 + b50 =L= 1;

e106..  - x51 + x81 + x83 + x85 + x87 + x89 + x91 + x93 + x95 + x97 + x99 =E= 0
       ;

e107..  - x54 + x82 + x84 + x86 + x88 + x90 + x92 + x94 + x96 + x98 + x100
        =E= 0;

e108..  - x52 + x101 + x103 + x105 + x107 + x109 + x111 + x113 + x115 + x117
        + x119 =E= 0;

e109..  - x55 + x102 + x104 + x106 + x108 + x110 + x112 + x114 + x116 + x118
        + x120 =E= 0;

e110..  - x57 + x121 + x123 + x125 + x127 + x129 + x131 + x133 + x135 + x137
        + x139 =E= 0;

e111..  - x59 + x122 + x124 + x126 + x128 + x130 + x132 + x134 + x136 + x138
        + x140 =E= 0;

e112..  - x61 + x141 + x143 + x145 + x147 + x149 + x151 + x153 + x155 + x157
        + x159 =E= 0;

e113..  - x63 + x142 + x144 + x146 + x148 + x150 + x152 + x154 + x156 + x158
        + x160 =E= 0;

e114..  - x65 + x161 + x163 + x165 + x167 + x169 + x171 + x173 + x175 + x177
        + x179 =E= 0;

e115..  - x67 + x162 + x164 + x166 + x168 + x170 + x172 + x174 + x176 + x178
        + x180 =E= 0;

e116..  - 10*b1 + x81 =L= 0;

e117..  - 10*b2 + x83 =L= 0;

e118..  - 10*b3 + x85 =L= 0;

e119..  - 10*b4 + x87 =L= 0;

e120..  - 10*b5 + x89 =L= 0;

e121..  - 10*b6 + x91 =L= 0;

e122..  - 10*b7 + x93 =L= 0;

e123..  - 10*b8 + x95 =L= 0;

e124..  - 10*b9 + x97 =L= 0;

e125..  - 10*b10 + x99 =L= 0;

e126..  - 10*b1 + x82 =L= 0;

e127..  - 10*b2 + x84 =L= 0;

e128..  - 10*b3 + x86 =L= 0;

e129..  - 10*b4 + x88 =L= 0;

e130..  - 10*b5 + x90 =L= 0;

e131..  - 10*b6 + x92 =L= 0;

e132..  - 10*b7 + x94 =L= 0;

e133..  - 10*b8 + x96 =L= 0;

e134..  - 10*b9 + x98 =L= 0;

e135..  - 10*b10 + x100 =L= 0;

e136..  - 10*b11 + x101 =L= 0;

e137..  - 10*b12 + x103 =L= 0;

e138..  - 10*b13 + x105 =L= 0;

e139..  - 10*b14 + x107 =L= 0;

e140..  - 10*b15 + x109 =L= 0;

e141..  - 10*b16 + x111 =L= 0;

e142..  - 10*b17 + x113 =L= 0;

e143..  - 10*b18 + x115 =L= 0;

e144..  - 10*b19 + x117 =L= 0;

e145..  - 10*b20 + x119 =L= 0;

e146..  - 10*b11 + x102 =L= 0;

e147..  - 10*b12 + x104 =L= 0;

e148..  - 10*b13 + x106 =L= 0;

e149..  - 10*b14 + x108 =L= 0;

e150..  - 10*b15 + x110 =L= 0;

e151..  - 10*b16 + x112 =L= 0;

e152..  - 10*b17 + x114 =L= 0;

e153..  - 10*b18 + x116 =L= 0;

e154..  - 10*b19 + x118 =L= 0;

e155..  - 10*b20 + x120 =L= 0;

e156..  - 10*b21 + x121 =L= 0;

e157..  - 10*b22 + x123 =L= 0;

e158..  - 10*b23 + x125 =L= 0;

e159..  - 10*b24 + x127 =L= 0;

e160..  - 10*b25 + x129 =L= 0;

e161..  - 10*b26 + x131 =L= 0;

e162..  - 10*b27 + x133 =L= 0;

e163..  - 10*b28 + x135 =L= 0;

e164..  - 10*b29 + x137 =L= 0;

e165..  - 10*b30 + x139 =L= 0;

e166..  - 10*b21 + x122 =L= 0;

e167..  - 10*b22 + x124 =L= 0;

e168..  - 10*b23 + x126 =L= 0;

e169..  - 10*b24 + x128 =L= 0;

e170..  - 10*b25 + x130 =L= 0;

e171..  - 10*b26 + x132 =L= 0;

e172..  - 10*b27 + x134 =L= 0;

e173..  - 10*b28 + x136 =L= 0;

e174..  - 10*b29 + x138 =L= 0;

e175..  - 10*b30 + x140 =L= 0;

e176..  - 10*b31 + x141 =L= 0;

e177..  - 10*b32 + x143 =L= 0;

e178..  - 10*b33 + x145 =L= 0;

e179..  - 10*b34 + x147 =L= 0;

e180..  - 10*b35 + x149 =L= 0;

e181..  - 10*b36 + x151 =L= 0;

e182..  - 10*b37 + x153 =L= 0;

e183..  - 10*b38 + x155 =L= 0;

e184..  - 10*b39 + x157 =L= 0;

e185..  - 10*b40 + x159 =L= 0;

e186..  - 10*b31 + x142 =L= 0;

e187..  - 10*b32 + x144 =L= 0;

e188..  - 10*b33 + x146 =L= 0;

e189..  - 10*b34 + x148 =L= 0;

e190..  - 10*b35 + x150 =L= 0;

e191..  - 10*b36 + x152 =L= 0;

e192..  - 10*b37 + x154 =L= 0;

e193..  - 10*b38 + x156 =L= 0;

e194..  - 10*b39 + x158 =L= 0;

e195..  - 10*b40 + x160 =L= 0;

e196..  - 10*b41 + x161 =L= 0;

e197..  - 10*b42 + x163 =L= 0;

e198..  - 10*b43 + x165 =L= 0;

e199..  - 10*b44 + x167 =L= 0;

e200..  - 10*b45 + x169 =L= 0;

e201..  - 10*b46 + x171 =L= 0;

e202..  - 10*b47 + x173 =L= 0;

e203..  - 10*b48 + x175 =L= 0;

e204..  - 10*b49 + x177 =L= 0;

e205..  - 10*b50 + x179 =L= 0;

e206..  - 10*b41 + x162 =L= 0;

e207..  - 10*b42 + x164 =L= 0;

e208..  - 10*b43 + x166 =L= 0;

e209..  - 10*b44 + x168 =L= 0;

e210..  - 10*b45 + x170 =L= 0;

e211..  - 10*b46 + x172 =L= 0;

e212..  - 10*b47 + x174 =L= 0;

e213..  - 10*b48 + x176 =L= 0;

e214..  - 10*b49 + x178 =L= 0;

e215..  - 10*b50 + x180 =L= 0;

e216..    x51 - x52 =L= 0;

e217..    x52 - x57 =L= 0;

e218..    x57 - x61 =L= 0;

e219..    x61 - x65 =L= 0;

e220..  - x53 - x56 - x58 - x60 - x62 - x64 - x66 - x68 - x69 - x70 - x71 - x72
        - x73 - x74 - x75 - x76 - x77 - x78 - x79 - x80 + 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;

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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